Yes, I think they are different things. The term "sex" relative to an individual refers to the structure of their genitalia. While the term "gender" relative to an individual refers to their sexual identification. But this is a difference that the simpletons and ignoramuses among us can't grasp, and so they get all upset and confused whenever a difference is being alluded to. And to multiply their ignorance, "gender" identification is subjective. Meaning that I might assign a different gender to person "X" than person "X" might assign to themselves, or from the gender that person "Y" might assign to them. Because gender assignment is just that: assigned. And it may or may not correspond with the structure of the genitalia of the assignee, or with the criteria of other people.
And that's the real difference: criteria. We all pretty much agree on the criteria for designating an individual's sex because it is objective. We do not all agree on the criteria for assigning an individual's gender because it is subjective.
How do I know this? Well, partly because we are having this discussion/debate. And partly because I have personally known people who's designated sex does not coincide with their gender assignment, by themselves, and/or by others. And because I am capable of understanding the difference between a label and the thing/person to which the label is being attached.