Could someone please explain the difference between a wave packet and a wave train? I have rummaged around online but have not been able to find a definitive definition.
The terms overlap but aren't exactly the same in everyday usage.
A wave train simply means a series of more or less equally spaced wave crests.
A wave packet generally means a collection of waves with neighboring wavenumbers, which interfere to produce an envelope of finite extent where the net energy is nonzero.
If the size of the wavepacket is large enough that it contains many wave crests, then you could also call it a wave train. However, you can also create a wave packet which only contains one crest, in which case it would be awkward to call it a wave train.
Likewise if you are at the beach and a series of nice, closely spaced wave crests come along, you would not tell your fellow surfers "dude, that's an awesome wave packet!"