heaving to and hoving to are completely different. As I recall (but i maybe mixing them up!) hoving to is an emergency heavy weather manoever with the idea that the boat is kept at an angle wrt to the on coming waves of about 45 degrees so that the boat maintains speed , rudder control and can roll over the waves. The other, heaving to, is a configuration in order that the boat can be left to sail itself by backing the jib and easing the main so the sailor can do other jobs. If you back the jib and ease the main in storm conditions very good luck to you. Just for further the confusion "bijdraaien' , in dutch is how the sails where traditionally set in good weather so the boat could be left to steer itself and bijleggen is what the dutch sailors did in storm conditions to keep the ship rolling over the waves at a angle.
I'm not familiar with the difference you mention (although I'm always happy to be re-educated). My perspective is that heaving to is the act of doing it, and hove to is the post-execution state. Heaving to, or being hove-to, is used to 'park' the boat (such as it can be with minimal forward or leeward progress) both during normal conditions (to take a break and/or reef a sail) and/or during heavier weather (to take a break and or calm the wave action).
Backing the jib and easing the mainsheet completely
, while lashing the tiller seems to work well on a C22 swing keel