There aren't exact thresholds, but hypersonic generally refers to speeds fast enough that fluid heating can no longer be approximated away and chemical reactions and ionization in the air start to dominate.

Aerodynamics is a practice of which physical phenomena you can ignore. At low speeds you can pretend the speed of sound is infinite / air is incompressible (these are equivalent), as you get faster you have to start paying attention to compression, then shock waves, heating, ionization, and the mechanics of individual particles.