'Because' does imply cause, 'since' can imply time or cause. What does that mean? It means that most of the time these words are synonymous and you can use either one:
'Since my dog is so hairy, I have to get its hair cut regularly.'
'Because my dog is so hairy, I have to get its hair cut regularly.'
Both of these sentences are correct. The only trap you have to watch out for when using 'since' is ambiguity:
'Since we had breakfast, we were filled with energy.'
This lets you wonder, were we filled with energy because of breakfast or just after breakfast?
Hope that helps:-)