Yes, MTC (Midi Time Code) and Midi Clock are different protocols.
Based on things I have used, Midi Clock appears to be quite common. But when using Midi Clock, it was not unusual for me to see "jitter" of the bpm, ie the tempo keeps varying up/down by small amounts. Hence, there are solutions such as this which purportedly can generate a solid Midi Clock:
https://www.expert-sleepers.co.uk/usamo.html