Dear Rob,
Sorry for the late reply. Gain typically means a lower-level arm-level gain, a few extra copies. Amplification refers to higher level, usually focal amplifications (many extra copies, ~5 and up). For example, look at EGFR in glioblastoma, which is focally amplified in more than 40% of samples. The nearby gene CDC14C is frequently gained (along with most of the chromosome), but never amplified.
The IGV screenshot below illustrates this.
I hope this is helpful.
Niki.