Inter-BSC handover: handover between cells on different BSCs.
Intra-BSC handover: handover between cells on the same BSC.
Both cases you described are inter-BSC handovers. However, the first case is also an inter-MSC handover.
I’m not sure what you mean by internal handover…maybe it’s your vendor’s vocabulary. However, I think an internal handover will be the same as an intra-BSC handover, and an external handover an inter-BSC handover.