I would say that radical feminism takes a traditional Marxist structural analysis where men are considered the oppressor class, and women the oppressed class, and posits this is on the basis of the material fact of their female bodies. In the most strict or classical versions, it calls this set of material disadvantages for women, or advantages for male bodied people, "the patriarchy." That's a set of materially identifiable causes.
Intersectional feminism is to radical feminism as neo-Marxism is to classical Marxism. In neo-Marxism it is no longer class that is the important category - and class understood as a description as a material relation rather than some kind of social construct. Instead it's immaterial, culturally constructed identity groupings, like race or "queerness" or whatever else you can come up with.
Similarly in intersectional feminism, instead of the physicality of the female body compared to the male body being the cause of the oppression of women, it is the identity/social construct of gender.
I do think there is a linking idea between these, because you will find many many people who are not intersectional or neo-Marxists, and may indeed see themselves as radical feminists, who have adopted an immaterial and almost spiritualized concept of "the patriarchy". It's become a kind of cause in itself rather than a description of a set of material causes. (It's a bit like the concept of the Invisible Hand in capitalism or the Treasury of Merit - concepts meant to describe a chain of causation are used as causative.)
You can see a similar change in the way the word racism is used that also is a mediator between what used to be called the civil rights discourse and modern "antiracist" discourse.
I think it's a very easy thing to do when you adopt these kinds of designations for disparate material causes, or brain tends to begin to think of them as a thing. I increasingly think this is a link between these kinds of traditional Marxist material analysis and the neo-versions which use that concept to create further, often completely imaginary, intellectual structures.