Using :map provides a list of all mappings in Vim. But, I am unable to search through the list. I am surprised to see it being opened in a different type of window
Don't be surprised. :map is not related at all with :help so there's no reason whatsoever to expect it to work like :help.
You can give :map an argument to narrow-down the listing:
:map ,
With the right values for wildmenu and/or wildmode, you can tab-complete :map:
:map ,
You can also list the current mappings with :
:map
You can also use the mode-specific variants of :map to get a more manageable list:
:imap ,
:nmap ,
:xmap ,
and so on…
But keep in mind that :map only lists custom mappings (made by you or your plugins). If you want a list of default mappings, check out :help index.