Correct, they aren't the same, but usually only larger airplanes (747-400, A380 etc.) have a first class and only for very long haul (> 12 hour?) flights.
See e.g. https://onemileatatime.com/emirates-a380-first-class-vs-busi...
See e.g. https://onemileatatime.com/emirates-a380-first-class-vs-busi...
I know people who fly first class between say, Heathrow and JFK, mostly for the VIP hand-holding at both airports, that can save you a lot of time.