I have done a mixture over the years. Some will be fixed term contracts (3-12 months usually) for a fixed daily rate.
Others have been your regular full-time employee contract. I was a normal member of the company I just happened to not work in the office (or very rarely, maybe once every 2-3 months I would travel and stay in a hotel for a night or two).
For contact work my daily rate does not change regardless of where the company is located. Obviously this can make me a little "cheap" in some places and very expensive in others. After each contract I will re-evaluate my rate. Usually if I find it a bit too easy to get work I up it.
Providing my rate is enough to cover all my bills and put what I want into savings I am good. I have never been too bothered about chasing that little bit extra. At least not constantly chasing. I have a pretty solid financial plan for the future that I am happy with.
When I joined a company as a full time remote employee my salary matched those of the employees I was working with. Obviously it was a fair bit less than what I could get doing contact work but that is a trade off I was willing to make for the stability at the time.