Facts of the case are the events that allegedly took place and led to the litigation (in this case, the importation of the two individuals).

Grounds are the legal considerations that support either side of the case.

The ruling (also called "judgment," "decision," and "finding") is the what the judges order based on the aforementioned factual and legal considerations.

In criminal cases, the finding of guilt or non-guilt, usually by a jury, is called a "verdict." The sentence is the punishment portion of the decision, sometimes decided in separate proceedings. In civil cases, there is no sentence, even if damages are awarded.

"Facts and Grounds" are the two bases in every case. You can google the expression with quotation marks to see how it is used. Here are a few samples:

Statement of Additional Facts and Grounds for Relief
http://www.cdt.org/testimony/000225ftcdcstatement.shtml

(3) If the facts and grounds alleged in the complaint are not sufficient to state a claim for costs and reasonable attorney's fees, the Commission may dismiss the petition after an informal proceeding.
http://www.ethics.state.fl.us/orders/1997/97-35fo.html

If the facts and grounds essential to a decision have been submitted by one party and if the party whose case is to be rejected has been afforded sufficient time to comment, the principle concerning the right to a hearing set out in Art. 113(1), will have been respected.
http://www.jpo.go.jp/shiryou_e/s_sonota_e/fips_e/epo/gee/cha...

incidentally, "proceedings" are the steps that take place in the judicial process from the filing of a lawsuit to the conclusion of the case.