Fundamentally they're very different, although in another sense they have a lot of similarities.
Spin is related to space-time symmetry. It tells you how a particle transforms under Lorentz transformations. For example, a spin-1/2 particle is measured to have spin up or down with respect to some direction in space, and spin-0 particles do not change at all under rotations.
An isospin symmetry transformation is something that relates different types of particles to each other. It represents a(n approximate) symmetry of QCD, but just involves flavors of particles and has nothing to do with space-time symmetries. An isospin transformation would transform an up quark into a down quark in the same way as a spatial rotation transforms spin up into spin down.
They are both described by the SU(2) symmetry group, though, which is why they are largely analogous and also that is where the name "isospin" comes from. Up and down quarks can combine to form hadrons with various isospin properties in the same way that spin-1/2 particles (including quarks) can combine to form composite states with various spins, with essentially the same math in both cases.