Rein is both a noun and a verb for guiding and restraining. You can use the long strap, or rein, on a horse to control its speed and direction, and you can rein in your own tongue by closing your mouth.
Rein rhymes with rain but the two words describe very different things. Rain comes down all over the place, uncontrolled, while a rein holds things in place or controls what comes out. As a noun, rein is often used as a plural word "reins" when talking about actual leather restraints used in horse riding, but a rein also is something non-physical like when you put a rein on spending by shopping less.