Of course not. You can buy one or both -- it’s entirely up to you.
Jewish ceremonies require a plain band, meaning one that is a complete circle and not “broken” with stones. But this doesn’t mean you have to buy them. Many couples exchange their parents’ or grandparents’ rings and then slip on their “real” wedding bands after the ceremony.
If cost is the issue, I would suggest buying wedding bands that you can afford and save up for a diamond wedding band for a special anniversary -- like your 10th, 20th or 25th.