The are not quite the same:
"A walk-in closet allows people to enjoy the experience of choosing the perfect outfit for the day. More importantly, walk-in closet’s design is not limited to time and era because each of walk-in closets have its own unique qualities that you may prefer."
"reach-in closet" (aka "closet"): "This type of closet is very common. It is usually found in corridors or bed rooms because it does not take too much space. The reach-in closet style is organized by shallow depth."
https://donpedrobrooklyn.com/closet-style/Como tradução alernativa, sugeri "closet com espaço de locomoção".