Not quite. Cushion, Strawberry, and Walnut are all genetically pea + rose. ("Walnut" in genetics literature.)
The various comb appearances were named before the genetics were understood, which is why we have some inconsistent names. A "single" comb can be large or small, with more or less points, standing straight up or flopping over. A "rose" comb can be large or small, with or without a point on the back, with or without little bumps all over. A comb with both pea & rose genes can be large or small, bumpier or smoother, but the breed descriptions call them by different names (cushion, strawberry, walnut) instead of having a single name for all of them.
Yes, V and Buttercup are cause by different genes than any of the others, and give semi-unpredictable results when crossed with the pea or rose genes. People have studied how V and Buttercup interact with each other, and with single combs, but how they interact with pea and rose is not figured out very well.