Bunkai is the practical disassembly of kata techniques. It takes the movement and applies it as exactly as the form permits (taking into account that: (a) the movement is often larger for clarity or completeness of a full motion, so that only a relevant portion is applied; or (b) the movement is executed with tension so as to signal anticipating resistance; or (c) the movement constitutes a compromise between multiple options that are all valid…etc., etc.). Oyo is the “practical application” for learning fighting against a resistant opponent.
It will vary from bunkai precisely because if anyone goes out into the real world expecting their rehearsed encounters to manifest exactly as per kata movements is basically living with a version of karate that cannot work. Imagine if a boxer didn’t adapt drills constantly because they expected set attacks only! Oyo might involve exploring ways of entry into the technique or logically extending the technique to likely or possible follow-up techniques or responses.
In other words, oyo attempts to place disassembled 1-step, literal bunkai in some sort of dynamic context (preferably a large variety of such contexts).Henka takes the process a step further by exploring variations.Oyo and henka are part of what makes bunkai useful: they apply the bunkai.
Without them you are left with useless pre-rehearsed routines.Whether anyone in Okinawa or Japan historically used these terms is irrelevant: they are useful labels now (unless one inclines to the view that arts and sciences don’t advance but reached their zenith decades or centuries ago, and their particular school’s stilted, untested “orthodox” 1-step applications are the only “real” ones…).Hironori Otsuka, wrote:"It is obvious that these kata must be trained and practised sufficiently, but one must not be 'stuck' in them. One must withdraw from the kata to produce forms with no limits or else it becomes useless. It is important to alter the form of the trained kata without hesitation to produce countless other forms of training."