Not really. 'I have to go', is more of a command or something absolute. (e.g. I have to go to the bathroom)
'I have to get going' , suggest it is a future event (e.g. I have to get going soon) The similarity is when you use the term, ' I have to get going now'. This is the same thing as saying ' I have to go'.
The other difference is you would not say 'I have to get going to the bathroom'