which vs type vs command -v

Ask which about cd and it tells you there is no such command:

which cd; echo "exit: $?"

exit: 1

Nothing printed, and a failure status. cd works perfectly well, so the answer is wrong in any useful sense, and a script that tests for a command this way will refuse to run on a system where everything it needs is present.

The reason is not a bug. which searches PATH for an executable file, and that is all it has ever claimed to do. cd is not a file.

A name at your prompt can be five different things

When you type a word, the shell resolves it against five kinds of thing, in a fixed order. type -t names the kind:

shopt -s expand_aliases
alias ll="ls -l"
greet() { echo hi; }
for n in ls cd greet ll if; do printf "%-6s %s\n" "$n" "$(type -t "$n")"; done

ls     file
cd     builtin
greet  function
ll     alias
if     keyword

Only the first of those is a file on disk. A builtin is compiled into the shell, a function and an alias were defined by your configuration or by the current session, and a keyword is part of the shell's grammar. which is a separate program that gets none of this: it is handed a name, it looks through the directories in PATH, and it reports what it found there.

The shopt -s expand_aliases line is only needed because these examples run non-interactively. At a prompt, aliases are already on.

What each one answers

Put the three side by side and the pattern is immediate:

shopt -s expand_aliases
alias ll="ls -l"
greet() { echo hi; }
for n in ls cd greet ll; do
  printf "%-6s which=%s type=%s\n" "$n" "$(which "$n" 2>/dev/null || echo -)" "$(type -t "$n")"
done

ls     which=/usr/bin/ls type=file
cd     which=- type=builtin
greet  which=- type=function
ll     which=- type=alias

which answers for one of the four. type answers for all of them, because type is a shell builtin and the shell is what does the resolving in the first place.

command -v is the third option, and it splits the difference deliberately. It prints a path for anything that is a file and the bare name for anything that is not:

greet() { echo hi; }
command -v ls; command -v cd; command -v greet | head -1

/usr/bin/ls
cd
greet

Check that before you capture the result. path=$(command -v cd) gives you the string cd, not a path, and running "$path" afterwards looks for a file of that name in the working directory.

Which to use

In a script, command -v. It is specified by POSIX, so it is present in dash and every other POSIX shell as well as bash, and it is a builtin, so it starts no process. The guard at the top of a script is the common case, and only the status matters:

for c in jq definitely-not-installed; do
  if command -v "$c" >/dev/null 2>&1; then echo "$c: available"; else echo "$c: not installed"; fi
done

jq: available
definitely-not-installed: not installed

At a prompt, type. It says more, and type -a shows every candidate rather than the winner alone:

type -a ls

ls is /usr/bin/ls
ls is /bin/ls

Two answers for one program, because Debian's usrmerge makes /bin a symlink to /usr/bin and both paths are on PATH.

which when you want the file and nothing else, on a system where you know it is a command you are asking about. type -P does the same job without leaving the shell:

type -P ls; type -P cd; echo "cd: $?"

/usr/bin/ls
cd: 1

Where the distinction actually bites

A function can share a name with the command it wraps, and inside it, command is what reaches past the function to the file:

ls() { echo "my ls"; }
ls
command ls -d .

my ls
.

Without command on the second line, the function would call itself until the shell ran out of stack. This is the standard shape for a wrapper, and it is also why a which ls that reports /usr/bin/ls can be perfectly true and still not tell you what will run.

Debian's which is its own program

Debian does not ship the GNU which. It is a small /bin/sh script from debianutils, it takes -a and -s and no other options, and it was deprecated in 2021 and then un-deprecated by a Technical Committee ruling. The which page covers what that means in practice, including the flags that are not there and the ones that are.