Biocomputers and neuromorphic computers both draw on neural information processing, but their physical substrates are different. A neural biocomputer uses living cells. Neuromorphic hardware implements brain-inspired computation in electronic devices.
Where they overlap
Both can use event-driven signals, local dynamics and architectures inspired by neural systems. Neuromorphic electronics can also sit beside living neural tissue as part of a hybrid platform.
The practical distinction
If cells have to remain viable for the computation to work, the system contains wetware. If the neural principles are implemented entirely in electronics, the hardware is neuromorphic.