The difference is that if you don't pay rent, it is easier and less expensive for a landlord to evict you than it is for a lender to foreclose upon you because you didn't pay your mortgage.
I would recommend that you speak to the lender get a copy of your credit report, find out why you were declined for the loan and fix the issues.
Also, if you have only spoken to a lender at a bank, I would also recommend that you speak to a couple of mortgage brokers. Every lender is different and some of the brokers may have investors that have less stringent criteria than a bank or that offer government programs that may be able to assist you.
Best of luck,
Renting might actually make sense in your situation, at least for the short term. I'd beware of creative financing or private investors because it's entirely possible you'll pay a lot more in financing costs and, in the end, find yourself in an even worse situation. At the same time, if you have been unable to qualify for a mortgage for credit reasons, you would do well to get some objective advise and help. A good lender or credit counselor will be able to help you develop a program aimed at improving your situation -- sometimes in as little six months to a year. You won't necessarily have to pay for that help, either as long as you work with someone who's not just anxious to sell you a mortgage or a house. You want to find someone who will look at your situation and help you discover what makes the most sense for you.
I do work in the area and would be happy to make a couple of specific suggestions for folks you could talk with if you'd like.