They do sound synonymous, but both are actually different concepts. I’ll try to explain these concepts in a way that I know.
Neural Adaptation
Neural adaptation is observed when there is a continuous and constant stimulus around us and our receptors slowly inhibit their responses to that particular stimulus. The important thing about this is that we could not control it over time. The best example for this is the human olfactory receptors. When you are exposed to a particular odour/stimuli for a very long time, (your own odour, the smell of your house and similar continuous stimuli), the receptors would hinder themselves to it and eventually ‘adapt’ to it. This means that the receptors send limited signals to the brain.
Check this (and this) article that deals with this concept.
Habituation
Habituation happens with stimuli that occur intermittently or periodically. Most of the habituation process is a bottom-up process, which means this is totally driven by the external stimuli. This could be controlled and changed by us to a certain level if we pay close attention to the stimulus that is being habituated. A good example of this is our ears tuning out some of the frequently heard noise at our home. In this case, the information is sent to the brain but ignored.
I hope this helps.
