"Standby" generator,
"Continuous" (duty) generator,
"Prime" generator,
"Emergency" or "Emergency standby" generator
These terms all have different meaning, but the terms are all (mistakenly) used interchangeably.
In the case of emergency generators, the difference is in how fast it starts.
In the case of the others, it how long, and how often, they are expected to run, and whether they are rated to handle an overloaded. (Example: A Prime may be rated to handle a 10% overload for 1 hour every 12 hours.)
You can think of a "Continuous" or "Prime" as being de-rated (for a longer life with more continuous (24/7/365) use at continuous load), or conversely, that a "Standby" generator has its rating "boosted" (and lifespan shortened) knowing that it won't be used very often, and has a variable load.
The same exact unit that is rated a 20KW Standby generator may be rated as a 18kW Prime or Continuous Unit. Unless limited by the size of a breaker, both can put out the same power which may be a lot more than 20kW. (Starting large loads is another issue.)
At the end of the day, these are just numbers, the lifespan will be determined by heat and/or the duration of that heat.
Same with the utility transformer on the pole. It may be stamped 30KVA, and is expected to have a 30 year lifespan running at 30KVA (depending on ambient temperatures). But you can pump more KVA through it. It can run 45KVA with no problem, but it may only have a lifespan of 15 years. 60kva may equal 1 years. 150kva may equal 5 minutes, etc....