No, they don't mean the same thing. To have the enjoyment (or perhaps better, benefit) of something doesn't necessarily mean you possess it, and indeed in a trust set-up you certainly wouldn't.

1) Prise de possession (achat, location)

There seems to be little doubt that « prise de possession » refers to the precise moment that the keys are handed over to the ‘owner’ or lessee. In French, ‘possession’ applies to both what we might loosely refer to as ‘ownership’ in English and to rented property. A lessee takes possession of the property.
The trickier point is the question as asked, whether there is indeed a difference between ‘prse de possession’ and ‘entrée en jouissance’. In my experience, there are a number of terms to describe this particular moment depending on your standpoint, your role and where you are on the timeline.
I shall look into this further later on. In the meantime, I would confirm the meaning of ‘possession’ to be in accordance with that indicated by Phil Goddard. It does not have the same meaning as in English here.

http://droit-finances.commentcamarche.net/contents/immobilie...

La prise de possession

La prise de possession des lieux se traduit concrètement par la remise des clés à l'acquéreur, qui se déroule généralement le jour de la signature de l'acte authentique, ou par la perception des loyers quand le bien est loué. Dès la date d'entrée en possession des lieux prévue dans le contrat, l'acheteur est tenu de payer les impôts et taxes afférents au bien. Quand la vente porte seulement sur la nue-propriété, la prise de possession est réputée faite le jour de la vente.


http://www.pap.fr/conseils/location/signer-un-contrat-de-loc...

Date de la signature et entrée dans les lieux

La date de signature du contrat n'est pas la date de début de la location : celle-ci est précisée dans le contrat et peut être postérieure à la date de signature. L'état des lieux, en revanche, doit être établi le jour de la prise de possession des lieux.


2) Entrée en jouissance

http://www.cnrtl.fr/definition/jouissance


3) Prise de possession = entrée en jouissance ?
Not sure. This source seems to suggest they are the same :
http://www.pap.fr/conseils/achat-vente/remettre-les-cles-ava...
L'entrée en jouissance ou plus précisément la prise de possession du bien pour lequel vous vous êtes porté acquéreur intervient le jour de la signature de la vente définitive chez le notaire, soit généralement trois mois après la signature du compromis de vente. C'est ce même jour que les clefs sont remises.
Le notaire convoque les parties au rendez-vous de signature. Ce jour « J », il est procédé à la remise des clefs. On dit alors qu'il y a « transfert de propriété ». Il y a dans ce geste symbolique le passage de propriété.
Mais qui dit « transfert de propriété » dit « transfert des risques » (assurance du logement: dégât des eaux, incendie, vol), prise en charge des impôts locaux, règlement des charges de copropriété. Il y a donc concomitance entre la signature de l'acte authentique et l'entrée en jouissance.
Nombreux sont les futurs propriétaires qui, une fois l'avant-contrat signé, s'imaginent être les nouveaux propriétaires, veulent les clefs pour commencer des travaux, entreposer des meubles, etc. Et nombreux sont les propriétaires réticents.


--------------------------------------------------
Note added at 44 mins (2011-11-11 19:17:44 GMT)
--------------------------------------------------

BUT... and this is a big but this is Switzerland. I am on slightly shaky ground here as my references are French. I shall look into the Swiss side of things, but have a question. See discussion.

--------------------------------------------------
Note added at 1 hr (2011-11-11 19:38:40 GMT)
--------------------------------------------------

I had origianlly intended to post this in the reference section ratehr than as an answer, but it is too long for that section.

'Prise de possession' and 'entrée en jouissance' in French are synonymous. Both describe the same moment, as my references illustrate. The followng terms in the list are also synonymous.

@ Phil
Opinions expressed as to the meaning of 'possession diverge'. I agree wholly with your on that one.

However, the term 'enjoyment' is the correct term for 'jouissance'. 'Possession' is not necessarily realted to title or ownership under English porterty law either. 'Possession' can be used quite safely here.

http://www.profitdata.co.uk/adversepossession_248959.html

'Possession' and 'enjoyment' are suitable ways of rendering the French 'possession' and 'jouissance' here. The terms are fairly synonymous in both languages in this context and translate sufficiently faithfully.

I would not opt for 'use' but stick close to the French original.



--------------------------------------------------
Note added at 15 hrs (2011-11-12 10:11:14 GMT)
--------------------------------------------------

You have put your finger on an important distinction. We had to get rid of the idea that possession was applicable to rented property and then this element can become clear. Each term listed can mean pretty much the same thing but as you indicate, where each is used in the same document this is to mark a distinction. Your example I a good one although I would make the follows comments :
The buyer ‘takes possession’ (under the terms of the contract of sale) the day he receives the keys. On that day, he does not ‘enter into enjoyment’ of the property as it is rented out.
The lessee ‘takes possession’ (under the terms of the lease) the day he receives the keys. He also ‘enters into enjoyment’ under the terms of that same lease on that day. It is only at the end of the lease that the buyer may subsequently be able to enter into enjoyment of the property.
As I suggested in my somewhat rambling answer below, terminology in law depends on the point of view and the moment in time when a particular event occurs. In effect, two individuals are ‘in possession’ but under different contracts, at different moments in time and with a different status as it were.
No doubt, the explanation as to why all terms are listed, to cover all eventualities. Effectively that makes me come down on the other side. Similar but not synonymous! The two terms should not be run into one in translation.


--------------------------------------------------
Note added at 15 hrs (2011-11-12 10:15:27 GMT)
--------------------------------------------------

The lessor (as titleholder, 'owner') enters into possession under his contract of purchase before the lessee's entry into possession under his lease. One precedes the other, without the former the latter would not come into being.

"Entry into" rather than "taking of" (which might sound somewhat contentious rather than consensual). For "entrée en jouissance" I have seen (and sometimes use), where a distinction is necessary, the term "inception of ownership rights" (which of course includes the right to enter into possession).

--------------------------------------------------
Note added at 1 day17 hrs (2011-11-13 11:52:29 GMT)
--------------------------------------------------

As usual, Gérard Cornu in his magisterial Vocabulaire Juridique, is very helpful. He defines “jouissance” as follows: “Bénéfices et avantages divers attachés à la possession (au sens large) d’un bien ou d’un patrimoine.
(a) Dans un sens strict, droit de percevoir les fruits d’un bien (les loyers d’un immeuble) sur sa seule signature et d’en disposer sans en être comptable (jouissance des revenus);
b) Dans un sens plus large, [jouissance] englobe la jouissance au sens (a) et l’usage (“usus”: droit de se servir personnellement de la chose, e.g. habiter un appartement)...." So, (a) is the strict sense and (b) the wider sense, comprising both (a) and the right to use the property personally, which corresponds to the right to “prendre possession”. Cornu defines prise de possession as: “Acte matériel par lequel une personne se met en possession”. An author who has used both expressions is probably a lawyer and is clearly drawing a distinction between (a) ownership rights in general and (b) the right to occupy the property when the owner chooses to do so. Most cases where confusion arises involve leases or tenancy agreements drawn up by estate agents (need one say more...). As Cornu goes on to say: (c) Dans certaines expressions courantes (I think by this he probably means estate agents’ documents), [jouissance] correspond même davantage à l’usage qu’à la jouissance dans le sens (a) e.g. jouissance d’un jardin, troubles de jouissance.