Discrepancy in number of points and number of values on tensor spaces

When trying to use ApproxFun to interpolate a function on Chebyshev-points and compute derivatives, I came across the following behaviour:

Define two spaces of Chebyshev and ultraspherical polynomials:

using ApproxFun
C2 = Chebyshev(0..1)^2
U2 = Ultraspherical(1, 0..1)^2

Project a function onto the Chebyshev space:

> fc = Fun((x,y) -> cos(π*x) * cos(π*y), C2)
> (length(points(fc)), length(values(fc)), ncoefficients(fc))
(190, 190, 185)

Transform to ultraspherical space:

> fu = Conversion(C2, U2) * fc
> (length(points(fu)), length(values(fu)), ncoefficients(fu))
(196, 361, 190)

According to the docs, values(f::Fun) returns the f::Fun evaluated on points(f), but that does not seem to be the case as the number of points and values are very different. I am wondering what exactly is happening here.

The result is similar when projecting onto the ultraspherical space right away

> fu2 = Fun((x,y) -> cos(π*x) * cos(π*y), U2)
> (length(points(fu2)), length(values(fu2)), ncoefficients(fu2))
(196, 361, 185)

I am also not quite sure why ncoefficients(f) is smaller than length(points(f)).

Start by reproducing the tensor-space examples with Fun, Chebyshev, Ultraspherical, Conversion, points, values, and ncoefficients. Inspect how these entry points represent points, values, and coefficients for two-dimensional spaces, then establish whether the behavior or the documentation is incorrect. Done means the discrepancy and the relationship among the reported lengths are clearly explained and verified.