I think UBI is different in that everyone is given a certain amount of money as a basic human right, and then people can be paid market rate for the work they do.

You're right about the security that UBI offers though, and I think that removing the minimum wage would go well with introducing UBI. In some developed countries without a minimum wage, unions set the pay rate for specific jobs, a similar arrangement happens in Australia, where people are paid according to industry agreements on the value of a worker.