What is the difference between using a MOVE block instead of a direct connection when an output is just to be assign the input value in a function block diagram?
The "wire" tells you that the boolean value computed by ladder code (AND, OR, ...) on the left, is used on the right. It doesn't cause any "memory" to change. (Your drawing just the wire makes the diagram confusing; you really should show the operators on both ends of the wire.)
The MOVE operator causes the content of one memory location, of any type, to be conditionally copied to another. Using the MOVE operator, you can copy an integer, float or other more complex value to a new destination; I don't recall if you can do a value coercion (e.g., int to float) also but I'd guess that varied from controller to controller. As a side effect, the MOVE operator copies the input boolean on the left side, to the output boolean on the right; most "block" like operators in ladder logic do this. But that input boolean controls whether the block actually does its action, or not. In your example, you show the MOVE block, but not the critical parameters: the from and to locations; the "wire" feeding it controls whether the move actually happens. So a better move example would be:
---| X |------| MOVE(P,Q) |---( Y )---
What this says is, "if X is true, then copy P to Q, and assign true (from X) to Y; if X is false, move nothing, and assign false(from X) to Y." (The boolean value of X is copied through the MOVE block).
Since MOVE will work with any type, you can use MOVE to copy a boolean value in a memory location to another location; just imagine P and Q above being boolean variables. However, boolean conditions and actions work just as well:
---| X |----( Y )---
copies the boolean value of X to the boolean value of Y.
To truly simulate a boolean MOVE command, e.g., "copy boolean P conditionally to Q if X is true" requires some convoluted boolean logic:
--+--| X |----| P |---+--( Y )----
| |
|--| *X |---| Y |---|
where *X means "not X". MOVE is simply easier to "write".