I think "on the go" is more likely to refer to being very busy and active, whereas "on the move" could refer to physical movement between locations (i.e. changing location), though could also be figurative. Referring to someone as being "on the go" may emphasise how busy they are and how much of a hurry they are in, whereas referring to them as "on the move" in a figurative sense could emphasise that they are starting to make progress or take action.

Hi Viviana. 'On the go' definitely refers to a person being very busy, doing many different things. For example, on Saturday I'm always on the go - I have to do the shopping, the cleaning, take my kids to football, etc. This is quite a common phrase, so this is the one to remember. 'On the move' is less about being active and more about moving from one geographic location to another. For example, traveling salesmen are always on the move from one customer to another. It can also be used to suggest that something is getting better. For instance, 'the economy / his career is on the move'. This is less common, but is grammatically correct. Thanks for your question Viviana, and I look forward to reading more of your posts.

‘On the move’ is most often used to mean ‘nomadic’ or ‘itinerant’. ‘On the go’ generally has the meaning of ‘energetic’ and has little to do with ‘going’. By the way, words in English are never ‘always interchangeable’ to someone who knows the language well.

The expressions are emphatic synonyms for "moving" and "going". The difference between the two is exactly explained by the difference between the verbs "to move" and "to go".