Abstractly, in the sense that "freedom from speech is not freedom from consequences", I don't think they're fundamentally different. If you're a free speech absolutist, then the nature of the relationship shouldn't matter. They're both just private organizations making choices about how they voluntarily associate with others.

Most people aren't free speech absolutists, though, and I agree that they'd think there's a fundamental difference between employer-employee relationships and user-provider relationships as a whole. But it should be significantly harder for an employer to fire an employee than for a service provider to ban a user.