As usual, that’s documented (we can RTFM).

• Bash command line editing covers searching.
• Readline library command line editing covers searching.

Before trying ctrl-s, you may want to disable software flow control: run stty -ixon & add it to your initialization files. Otherwise, you’ll pause terminal output. ctrl-q resumes terminal output.

stty reveals terminal special characters

$ stty -a
⁝
intr = ^C; quit = ^\; erase = ^?; kill = ^U; eof = ^D; eol = <undef>; eol2 = <undef>; swtch = <undef>; start = ^Q; stop = ^S; susp = ^Z; rprnt = ^R; werase = ^W; lnext = ^V; discard = ^O; …
⁝

These special characters/keys often perform special functions. To illustrate

• ctrl-d on empty input typically exits/logs out of interactive terminal applications (including shells)
• ctrl-u discards input (useful for inputs like password prompts that don’t echo input back)
• ctrl-v inputs next character literally (such as tab)