I find it annoying in the UK that modern over here is actually jazz or modern theatre and very few schools I've seen teach comtempary which is American modern!
Usually if it's not a syllabus class or it's an adult class it's jazz.

I'm an adult dancer and would love to take classes in both contempary/modern and Jazz but it's just findng the classes!

This is a great posting because no only can dance types be defined in terms of what they are trying to convey but by their history. You did that here with bringing up Martha Gram and Isadora Duncan. I would also like to point out that the difference dance forms can also be classified in terms of what their emphasis is. What I mean by that is, ballet is emphasizing line in the body. While modern dance emphasizes the shape that your body makes when you dance. I'm a double major my second major being fashion design but I had to take a class in "Fundamentals of Design" and it really helped me to apply this concept not only to the way that I look at my designs as a fashion designer but when I look at all art forms because we learned about the elements and principles of design (shape, form, line, proportion etc). Applying this to dance, one can see how each element is applied and therefore come to a conclution about which dance form is being used. The elements of design in art are to dance as a medium (oil paint, acrylic paint, watercolor etc) would be to a painter. I thought that was a pretty cool finding.

i know your not looking for what it is but a short version of what you said is modern is a slower version of jazz

thankyou