I do not think there is value in differentiating bool and boolean. I note there is a distinction between "int" (limited range, overflowing) and "integer" (abstract mathematical concept)...but none between "float" and "floating-point" (perhaps there should be "real-number"?)
There are some questions with titles to the effect of "is there a difference between bool and boolean". But they seem to be language-specific, and I doubt there's much discernment in using the tags in the general case. Examples of the few specific differentiating discussions, which I think would be fine tagged merely by "boolean" and the appropriate language tag:
Sidenote: I am asking this question here in part to draw increased attention to the rather silly requirement of having 5 reputation in this tag to use the automated tag synonym suggestion mechanism:
Logically speaking (er...pun intended?) it would seem that whatever reputation it takes to retag a bunch of questions manually should be greater than or equal to the reputation to make a tag synonym suggestion. In a system that can triage wiki-like suggested anonymous edits from the Interweb, why would a tag synonym suggestion trigger a "nope, you can't do that" dialog to someone who can retag?
Then again, discussion is good.