Linux command to list all available commands and aliases

You can use the bash(1) built-in compgen

• compgen -c will list all the commands you could run.
• compgen -a will list all the aliases you could run.
• compgen -b will list all the built-ins you could run.
• compgen -k will list all the keywords you could run.
• compgen -A function will list all the functions you could run.
• compgen -A function -abck will list all the above in one go.

Check the man page for other completions you can generate.

To directly answer your question:

compgen -ac | grep searchstr

should do what you want.