Libery is not A licence (or license in American English). I think this is a Christian saying. It has to do with the difference between these two freedoms. From what I understand, liberty assumes that one behaves freely according to moral codes of the soiciety, without infringing on the rights of another. It's like the First Amendment to the US Constitution guarantees you free speech etc. there are laws that do not allow you to be nuisance to others, touch them however you want, hit them, rob them and so on. A license would let one do what they want, versus the liberty allowing you to do what one should. There's a possible endless discussion behind this but I think that's it, in a nutshell.

"Licence" means excessive freedom. So the sentence means that your freedom allows you to do things within reasonable limits. Freedom doesn't mean you can or should go to extremes.

freedom doesn't mean you can do whatever you want even it brokes the rules. licence=indulgence.

I would see this as meaning "Having liberty is not a licence to do exactly as you please" i.e. although society may allow you a lot of freedom in your life there are still limits so, for example, you don't have the freedom to kill anyone you want (we would hope!).