What is the difference between family mediation and relationship counselling?

Mediation tends to be used to resolve a relationship issue or a child custody issue after separation so the parties avoid having to go to court- the hope is that going through a mediator (which is a type of lawyer) will make the parties agree so a judge doesn't have to decide for them. I think relationship counselling sounds more what you want if you want the relationship to continue and you just need to work on why you are having problems and come to the bottom of where the problem lies.
This is the case in the country I live in, it might differ somewhat in other countries though. I hope this helps you and good luck. :-)