If they vary, how are they categorized?
They are not.
LCDs have virtually no standards associated with them. There are no names for interface types, they use different signals and timing, they are virtually all propitiatory. That is why your questions have no answers.
Some processor chips like the ARM chips used in mobile phones have configurable LCD drivers to allow a large number of different types of LCD to be accommodated but not all types.
Most LCDs are obsolete in 6 months, you can get industrial ones that have a longer life but not over 3 years. Then the remaining stocks are dumped on the surplus market and when they are gone they are gone.