what is the meaning difference between
I'd better go and I'd better be going Does the first one means I must go now and the other I should begin to think to leave
I think you're right, 'I'd better go' sounds a little more abrupt and sudden than 'I'd better be going', which sounds a bit softer.
I'd better be going will pretty much only be used for a (probably pre planned) exit from a social gathering or whatever and generally is a way of saying 'I am about to go', whereas I'd better go can also be used for things like if your house is on fire and you realise the flames have reached your room, you might say 'I'd better go!'. So I'd better go can be you literally saying you need to go/making the decision it would be best for you to go and it generally means there will be a REASON why you now need to go, not just a way of announcing your imminent exit.
But I think by and large they are interchangeable.