I’m not sure you can do
kill 1 (or rather, you can try, but you won’t be allowed to, unless your root, and then you’re in for a surprise).
1 here always refers to the process with id 1, which is usually
init (or some variant thereof).
To actually answer your question, if you’re in a shell which supports job control,
kill will be a shell built-in, handling both cases (managing jobs and processes). See for example Bash’s
If you’re in a shell which doesn’t support job control (are there any?),
kill will be a binary in the system, typically
/bin/kill; see for example
kill command. Even in a shell with a built-in
kill command, you can access this one for example by specifying its full path. This
kill command is also accessible without a shell (for use from another program).
See also POSIX’s definition of
kill, which covers both cases (but doesn’t specify what is implemented where).