Having learnt some basic differential geometry, I know that (upto details) we define differentiable manifold such that any 2 maps on it are compatible, in the sense that the transition map between them is differentiable. When we define varieties in algebraic geometry, we speak (again, up to details) about a ringed topological space that can be covered by open subsets, all isomorphic to affine varieties, with another property of compatibility: regular functions defined on subsets $U_1,U_2$, which agree on the intersection, glue together to a regular function on the union (this is just by the definition of a sheaf).
I think that we can interpret the open affine subsets of the variety as giving local affine coordinates, by the isomorphisms. Is it a good intuition to keep in mind? If it is, in view of that, can we also interpret the gluing property in a way similar to the differentiability of the transition maps?
Thanks in advance!