Last winter the heat wasn’t keeping up with the set temp, the outside fan came on, but the compressor would not start, you could hear it trying to start but it wouldn’t come on. The tech said the compressor was short cycling, and it was now "locked up", they put in a new compressor (part was cov’d as unit only 5 yrs old, but labor wasn’t) and a new capacitor and that did the trick.

This spring, put on the a/c, and it wasn't getting cool, went outside and this time the fan wasn't on. Did a troubleshoot with tech over the phone, had the cover off the outside unit, checked a few things as he instructed, and when I pushed the cover back on, it kicked the fan on, tech said probably a loose connection somewhere and they would have to come out. They came out and found a loose terminal on Y1, of the defrost control board and said that was causing the compressor to cycle on and off rapidly, at this time the fan was working and the house was cooling, but eventually the board would fail altogether. We did not want the compressor to be affected by this, so we told them to replace the defrost board.

I am new to heat pumps with central air. Were these 2 problems related? I ask because each time they said compressor short cycling. I just want to make sure the problem is fixed for good. Don’t want the compressor to fail again.

There was a preventative maintenance & cleaning done as well, and they said everything else was working fine.

Yes the two problems were likely related, but not to worry, although you took the long road, both parts were replaced and the unit should be reliable. I would like to look at the compressor contactor (the switch that turns the compressor on and off). If the unit indeed short cycled, that switch may fail prematurely. I am sure, however this was checked with the preventive maintenance.