The difference is that with common law, you have to show sufficient evidence of at least on year cohabitation. If you are married you don't have to show all that but you still need to show proof of a genuine relationship. Even though we were married, we approached the application as if it were a common law application still. We sent copies of our drivers license showing same address, proof that we had each other as beneficiaries on our life insurance plans at work, copies of bank and credit card statements. We sent one that showed the date the account was opened and one of the most recent ones to show they were still open at the time of PR application. We also got letters of support from his family and friends as well as mine too. We sent copies of letters addressed to both of us from the daycare our child attends as well as from the City of Toronto. For some reason, we realized at the end that I'm not on the lease even though we thought I was... so we got our building to write a letter stating that I am living there for how long.
As for the marriage cert... which province are you in? I applied online and got mine in about 2 weeks. I was going to wait the 12 weeks they said but I wanted to try online anyways and see how long it would take. After the ceremony we get a paper (I think solemnization or something of the ceremony) that had the registration # and that's what we needed to apply for the marriage certificate. If you want to wait until after the ceremony you can choose to but you're not sure how long it will take to get the cert. Also, if I were you, I would want to send the info to them ASAP so as not to delay further. Good luck with all and if you have anymore questions don't hesitate to ask.