Why are counters in a PIC or other MCU called timers?
A real timer counts time elapses, timer don't have bits, so to speak.
They are really just counters, 8-bit or 16-bit presettable counters. All electronic parts with such function are correctly called counters, like 7490, 4040 or 4060...., have anyone ever seen a 4-bit binary timer? I have a frequency counter, it also measure time interval, but it is never called a timer.
As Papabravo said, a counter is triggered and not a fixed interval of time. Though an MCU's timer may be triggered externally and also can be adjusted to a different interval at will, the timer is still is a specific interval and does occur in the background.
Disassemble a digital real timer. What do you find at its lowest core? Digital bits or quantum packs of time?
to me the crux of it is that timers are counters driven off of a periodic source. You start a timer, then sample the count at a given point and that is the elapsed time in periodic units. Seems like a timer to me.
OK...I'm not sure where you are going with this but you won't get either an argument or strong support for your position from me. Timers and counters are both great!
Not on it's own, but the 'timer' in a PIC isn't just a counter, it has extra hardware as well - so those counter chips, plus others, could be called a 'timer'
Anyway, this is a silly question and the answer is "who cares".