How to test if command is alias, function or binary?

If you're on Bash (or another Bourne-like shell), you can use type.

type command

will tell you whether command is a shell built-in, alias (and if so, aliased to what), function (and if so it will list the function body) or stored in a file (and if so, the path to the file).

For more information on a "binary" file, you can do

file "$(type -P command)" 2>/dev/null

This will return nothing if command is an alias, function or shell built-in but returns more information if it's a script or a compiled binary.

References

• Why not use "which"? What to use then?

The answer will depends on which shell you're using.

For zsh, shell builtin whence -w will tell you exactly what you want

e.g.

$ whence -w whence
whence : builtin
$ whence -w man     
man : command 

In zsh you can check the aliases, functions, and commands arrays.

(( ${+aliases[foo]} )) && print 'foo is an alias'
(( ${+functions[foo]} )) && print 'foo is a function'
(( ${+commands[foo]} )) && print 'foo is an external command'

There's also builtins, for builtins commands.

(( ${+builtins[foo]} )) && print 'foo is a builtin command'

EDIT: Check the zsh/parameter module documentation for the complete list of arrays available.