I'm a masochist and get sexual pleasure from pain; that's wired into me. I'm also submissive. It's who I am. For me, these two things go together.
It's not always the case. A huge misunderstanding is that you have to like pain to be submissive. Masochism is a part of your sexual identity; you either have it, or you don't. No one can make you like pain, but you can learn to accept pain for your Dominant if that is your wish. Doing so does not make you a masochist. Masochists come in all forms. The majority are submissive; however, I know several Dominants that like pain and instruct their submissive to give them pain during play. Switches are known to like both, but that isn't always the case.
I read about submissives forcing themselves into play with Dominants because they think it comes with the submissive role. They don't understand that they are separate entities. Now, submitting to pain to please the Dominant is different and can bring your further into your submission the more you take from your Dominant, but it's not required and should never be forced.
Masochism is about pleasure, pure and simple. It has nothing to do with punishment, which is used to enforce behavior. No one likes to be punished, but sometimes if the dynamic agrees to use punishment, it's a necessary evil.
If you are a submissive or learning about submission and don't like pain or don't think you want pain play, that doesn't mean you aren't submissive. It just means you aren't a masochist. There are so many roads to submission that going down that one is not required. There are endless possibilities.