There are a few -c- vs. -s- word pairs kicking around, and I’m sure we’ll cover them all in the fullness of time. We’ve already looked at “practice” vs. “practise”, and in fact this one both follows the same basic rules and bears the caveat that things are oh, so different in American English – so this post applies to British English only.
The difference again comes down to whether you’re using the word as a noun or a verb.
Licence is the noun (like our football practice). So you have a driving licence, or licence to kill. The second definition, which is actually packed into “licence to kill” with the first meaning, is freedom to behave as one wishes, without restraint. “They took the wild music as licence to dance until dawn” – you can see that the meanings are very close.
License is the verb – to grant a licence to or authorise something. “He is now licensed to drive a car – the DVLA licensed him and he has a driving licence.” By extension, we have a licensed premises (the licence to sell liquor has been granted to it) run by a licensee.
Just a little spelling quirk – if you’re licentious (disregarding rules; in the Oxford definition, rather sweetly, especially rules around sexual promiscuity OR grammar!) then it’s spelled like that, with the t. Like a practitioner who practises something (in a doctor’s practice, for example).
You can find more troublesome pairs here.