What does this sentence actually mean?

They are equivalent. Some people may trouble about the commas in the second one but they say the same thing. They are so close that there is hardly a reason to choose one or the other. One being used rather than another could depend on the emphasis you wish to make. Whether the continued pain etc. is important or the nature of the additional treatment. The choice may also depend on whether the audience could understand the first sentence. As you have had some question you would know where it is being read. Further context would help make the choice clear.

Many patients continue to have pain and limited function and require some other forms of treatment.

The sentence above indicates that the current patients already have an issue and require treatment.

Many patients who continue to have pain and limited function, require some other forms of treatment.

The sentence above indicates that there are no patients with issues or you have not yet identified them, once they're identified, they will need to be treated.

Patients who continue to have pain and limited function may require some other forms of treatment.