Question

how are protist thought to have given rise to multicellular organisms

Answer 1

In general, the different between a colonial protist and a multicellular organism is that all the cells in the protist are the same, although some of them assume different roles when they all mass together. The cells of a multicellular organism are actually specialized in structure and form, as well as specialized to a greater extent in function.

It is a hairy definition and not everyone agrees with it, for sure.

Answer 2

To add to what @blues posted, the two characteristics that I learned that define a multicellular organism are cell specialisation/differentiation, and actual connections between the cells: they're not just stuck together and doing their own thing like in a colony of single-celled organisms.

Another thing: the transition from single-celled organisms to multicellular organisms can be observed in a lot of different taxa. In other words, it has evolved separately, multiple times.