MIDI Beat Clock
The MIDI Beat Clock signal works pretty simple, it sends 24 tick signals for each quarter note. A start signal is send to indicate when to start playing. From that moment on, the MIDI slave has to keep track of the ticks.
The problem is that small delays in the tick signal cause speed (BPM) variations. Missing ticks can make a MIDI slave run out of sync. The BPM value tends to jump around all the time with sometimes deviations of over 2 BPM.
Once the MIDI slave has gone out of sync it requires a re-sync. There is no way to detect that it is out of sync because the MIDI Beat Clock uses a relative value that every slave needs to keep track of.
A re-sync has to be done manual. But applications like Ableton Live will simply wait for a new start signal to be triggered. When the MIDI Beat Clock master is Ableton Live, there is no way to retrigger the start signal without interrupting audio playback.
MIDI Time Code (MTC)
The MIDI Time Code signal sends an absolute time position according to the SMPTE Time Code standard. This means that at any time all MIDI slaves know where they should be. Even if there is a short interruption, the next correct SMPTE Time value will tell the software where it should be.
Because MIDI Time Code is not telling anything about beats you can sync MIDI slaves with different BPM values. Thus every MIDI slave maintains its own tempo which is synced to the MIDI Time Code position of the master.