Like Audio gear, where output is measured in 'Watts' [RMS]-[PMPO], Engine power has more than one measurement 'method' depending on how much you want to fudge the results....my first car was 10 [RAC] horse power, which equated to about 33 BHP [measured at back wheels].
Bench Dynamometer tests often run the engine only and ancilliary power use for alternators, water pumps etc are handled externally, so the Bench Horse Power [also 'BHP'] will be a fair bit higher...just not 'realistic' when that same motor is designed around crappy, power-draining ancilliaries.
BTW....'RAC' HP was related to swept volume [capacity] and was for taxing purposes, not performance, as such.
Generally, BHP ratings claimed by manufacturers are 'optimistic' at best and down-right deceptive at worst.
Besides...it all matters how the car actually 'goes'...my old VF hardtop [Chrysler] - 225 cu.in. slant six with 160hp went a lot better than the VJ Charger [Chrysler] 245 cu.in Hemi six with 165hp....simply because the VF had a 2-barrel carb and the second throat felt like a turbo coming in...
BTW...with me in Motor racing, of course I'm a bit of a 'Petrol-head'....my first engine swap was at the age of 10....38 years ago...