My dictionary gives all of the "go on", "carry on", "keep on" as the same synonym for "continue". There was no difference to me till now. I need to write a sentence like:
We have decided to [carry/keep/go] on using free version of this software.
And [go on] does not sound comfortable to me in this case. Am I right?
go on
is often gets used to spur someone or something to start.
Don't wait for us, go on ahead.
In your case you are continuing to do something
keep on (AmE)
carry on (BrE, AmE)
are both appropriate.
Basically they mean the same thing, but in some contexts one usage is more common. The best choice is really context dependent.
That is a great story. Go on.
and
Q. Am I doing this correctly?
A. Yes you are. Carry on.
and
I asked her to go out with me, but she only laughs. But I will keep on trying.
