Why does the amplifier become a hysteresis comparator after adding positive feedback?

Don't be entangled with these superficial concepts. Comparators should be defined in terms of function, and are essentially amplifiers.

Comparators and op amps can be regarded as one kind of things, but there are more limits. If the op amp is connected to a comparator, that is not a problem.

In principle, the principle is similar. Compensation is omitted inside the comparator. Circuits such as analog bias are the comparators. The comparator requires speed, and the operational amplifier requires stability. The two can be interchanged if the requirements are not high. Generally, the comparator is OC output.