I appreciate that wikipedia may describe it like this, but that doesn't make it an accurate description used in chemistry.

This paper, for example, specifically looks at the differences between chemical and hydrogen bonding (specifically by look at bond strength).

>But I get some feeling that even ionic bonds are not "bonds" in your mind, only covalent ones?

I'd argue that the distinction is more categorical than physical.

All chemical bonds are covalent bonds, there's just a disparity in how much the electrons are actually shared.