`Vim: What is the difference between the remap, noremap, nnoremap and vnoremap mapping commands?`

remap is an option that makes mappings work recursively. By default it is on and I'd recommend you leave it that way. The rest are mapping commands, described below:

:map and :noremap are recursive and non-recursive versions of the various mapping commands. What that means is that if you do:

:map j gg
:map Q j
:noremap W j

j will be mapped to gg. Q will also be mapped to gg, because j will be expanded for the recursive mapping. W will be mapped to j (and not to gg) because j will not be expanded for the non-recursive mapping.

Now remember that Vim is a modal editor. It has a normal mode, visual mode and other modes.

For each of these sets of mappings, there is a mapping that works in all modes (:map and:noremap), one that works in normal mode (:nmap and :nnoremap), one in visual mode (:vmap and :vnoremap) and so on.

For more guidance on this, see:

:help :map
:help :noremap
:help recursive_mapping
:help :map-modes