How do zener diodes, silicon diodes, and base-emitter junctions differ in reverse breakdown mode?
You are correct as far as the data sheet ratings go.

Reverse breakdown in all 3 cases is avalanche - zeners less than about 7V use different mechanisms, but your example is 10V.

Breaking down the 1N4148 will not harm it provided the current and dissipation are limited. That is how you test the actual breakdown voltage with a curve tracer.

It's a bit more complicated with the BE junction- it will typically work as a 9V or so Zener but the transistor beta may be degraded over time, so it's best to avoid breakdown if beta is important.