Is 'cat' a shell built-in or an external program?

type tells you what the shell would use. For example:

$ type echo
echo is a shell builtin
$ type /bin/echo
/bin/echo is /bin/echo

That means that if, at the bash prompt, you type echo, you will get the built-in. If you specify the path, as in /bin/echo, you will get the external command.

which, by contrast is an external program that has no special knowledge of what the shell will do. On debian-like systems, which is a shell script which searches the PATH for the executable. Thus, it will give you the name of the external executable even if the shell would use a built-in.

If a command is only available as a built-in, which will return nothing:

$ type help
help is a shell builtin
$ which help
$ 

Now, let;s look at cat:

$ type cat
cat is hashed (/bin/cat)
$ which cat
/bin/cat

cat is an external executable, not a shell builtin.

cat is hashed (/bin/cat) is just like cat is /bin/cat (that is, it's an external program).

The difference is that you already ran cat in this session, so bash has already looked it up in $PATH and stored the resulting location in a hash table so it doesn't have to look it up again in this session.

To see all the commands that have been hashed in your session, run hash

$ hash
hits    command
   2    /usr/bin/sleep
   3    /usr/bin/man

$ type sleep
sleep is hashed (/usr/bin/sleep)

$ type man
man is hashed (/usr/bin/man)

$ type ls
ls is /usr/bin/ls

$ type cat
cat is /usr/bin/cat

$ type echo
echo is a shell builtin

You can also use the command whereis that is more efficient because it shows where the command is on the machine like also the manual pages library, etc..