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.
I think you are imagining this difference. The phrase "hoving to" is not used by the community.
If you back the jib and ease the main in storm conditions very good luck to you.
This is a difference in sail trim. Reaching is reaching, regardless of how your sails are configured to make that happen; in light wind you might use a spinnaker and a full main; in heavy winds, maybe just a small jib. Similarly, heaving-to is heaving-to, regardless of what sail combination you use to achieve it.
I would also point out that the goal of surviving a storm and taking a break for lunch are the same kind of goal: the crew wants to rest and not have to actively manage the boat for a little while.
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.
So, those words may refer to sail configurations, but "heaving-to" does not. It happens to be the case that heaving-to often involves backing an appropriately-sized jib, and doing something or other with the main, and so people have a tendency to use the term to refer to the sail configuration, but that is not correct. If you put your sails in a "hove-to configuration", but you end up making 5 knots of headway with very little leeway, you are not hove-to.