Hi David,
Connect Objects (with optional Delete)
If you have two or more polygon objects, then some options might not work. Like building “bridge” polygons among them, with real connections, instead of just visible (it looks connected, but an deformer might separate it.
Also, to have many objects with different axis position might not work very well, e.g., as clones. Note here that the each axis represent the “world-system” for the points of an object. To run the optimizer after such might be mandatory.
Current State to Object
The simplest case would be an object that is generated, (and/or) deformed and perhaps otherwise treaded. Additionally perhaps with options that needs to be done each and every frame as well, hence it might take a lot of time.
Besides that, there is a hierarchy/priority in set ups. Once it is a polygon object, the problems of priority are much simpler. It typically creates a polygon copy. To run the optimizer after such might be good.
Connect Object (from the Array menu)
It is the “Swizz Knife” for a lot of problems, but typically, think of a Generator which produces a new single object out of many. Note that it is a process that needs time, each frame. Simplified: if connects objects without the need to commit to it (as in “final”) and it has an option to “melt” points, without deleting the double (multi) points.
In MoGraph, I use it for example to connect all clones of a Cloner (often single polygon objects) to have one Object that can be used in a new Cloner in the Object Mode.
If in doubt, keep the original objects.
There is certainly more, but I hope I could shed some light on the main differences. If you get to a point where you don’t know, share a simplified file and mention your target. I’m happy to have a look into it.
All the best