CTRL+L and clear command do two different things (at least when using Bash on Debian):

• CTRL+L scrolls the terminal output one screen so you don't see your previous output, unless you scroll up;
• clear does indeed clear terminal output completely, and your previous command history is available only through the history command.

If you want CTRL+L to clear your screen completely you can add following to the .bashrc (or other file that is sourced when starting Bash, e.g. .bash_bindings):

bind -x '"\C-l":clear'

Note that it might not work if you use Vi mode inside Bash, but who does that.