Yeah that's my recollection too. The areas where they are likely to exist overlap, and that's what a bond/interaction is. The trouble with this stuff is that every year you studied it they told you that what you learned last year was a complete simplification and not really representative of what really happens!

Orbitals are actually an approximation, which is what part of the confusion is. The exact math is beyond me, but the idea is that the orbitals represent the most likely place for an electron to be, not the only place. Lots of probability involved, including with how electrons react with each other. Chemical reactions that do happen are just the most likely event, but when you atom by atom things can get really weird. At that scale electron don’t really obey classical physics (which is what intuition usually expects). As a more concrete example, if you take a chemistry class, you probably learn that electrons like to group in pairs of two, which is weird if you think about two negative charges grouping together, but (once a gain with math that I don’t claim to understand) quantum physics does explain this (because of electron “spins” which do not spin like in a classical physics sense) even though it is not intuitive from classical mechanics. Similarly orbital rules break down at some points, such as carbon able to to have 4 bonds (the s and p orbital have very similar energy levels if I remember the chemistry right), which you can’t get from the simplified orbitals.