In Terminal, how can you determine which shell is actually running?
It depends on the shell you are running in.

If it is a POSIX confirming shell e.g. bash, ash,ash, sh, and some others e.g.  csh, tcsh then echo $0 will return the shell's name

e.g. 

~ $ bash
bash-3.2$ echo $0
bash


or 

~ $ ksh
$ echo $0
ksh


However not all shells are POSIX e.g. I used to use ipython shell profile and now fish