I have put two engines on two different airplanes that I have owned, Both running the LYC-O-360 engine.
The TBO is time between overhaul. Most modern engines will use 2000 hrs. some of the cont have 1500 but most of the 1200 guys are out of the fleet, there is an AD that is done at overhaul time to bring it up to 2000.
A-IO-360 have a 1000 hr TBO, because it is an aerobatic engine.
The reason the 2000 hrs is there for part 91 is only a suggestion. if you maintain your engine well, know how to operate it properly, live indoors (hanger, change the oil every 25 hours, not every 50, and take care of it during the start up, (preheat when under 40-50deg) it will run well past 2000hrs.
the 2000 hrs DOES however come into play at flight schools. as does the 100hr inspection etc...
in 1996/7 I paid 11k to have a Overhauled engine put on, in 1999 it was 18k, but I upgraded much of the engine and went to **THE** shop to do it. I expect my engine to make it to 2500 hrs and maintain good compressions.
Also, if you buy a 20 year old airplane that has 1000 hrs on the engine, and has only been flown 10hrs a year for 10 years, that engine is garbage, plan on getting a new one.