Is there a difference in meaning when used in a technical context? For example, does a fork latch in a recess when pressed or does it catch in the recess?
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"settles" in a groove has a more permanent connotation than "catches" in a groove, which, to me, seems more like "snags".
The verb latch is today used only with on following it, not with in, like:
The OED says that using latch to mean to catch in something like a receptacle is now obsolete or dialectal, and provides these old examples:
There is another dialectal use meaning to alight or settle, as in:
I strongly encourage you to use catch here, not latch, unless you are trying to represent dialect or archaic speech.
If there is no mechanism that holds the forks in place, if they just stay fast by design, I would use the passive construction "are secured."
"Until the forks are secured in the recess" makes it clear that, by whatever method of retention, the forks maintain their position in the recess.
So far as I'm concerned, the brackets there (the horizontal supports under each shelf) latch into the standards (the long vertical slotted strips fastened to the wall).
In this particular example there are lots of "recesses/grooves" in the uprights. But in, say, a track lighting system, the bulb holder may fit into an extended groove - in which case you normally latch it in by pushing it in in one orientation, then twisting it by 90° to secure it.
Here are some written instances of "which latches into", where in most cases it's fairly obviously describing some physical component being "locked" into a position within an assembly.
To my way of thinking, catch usually implies inadvertently get caught up/snagged, so I wouldn't use that word in OP's context, where latch, lock, click, snap are all reasonable alternatives.
Having said that, in the "negative" version of OP's example, I think catch can actually work better. Suppose he's trying to secure his "locking fork" into the "locating recess" - but failing because of clumsiness / manufacturing defects / worn parts / whatever. In that case, he could quite reasonably say "Fiddlesticks! I can't get the fork to catch in the slot!"