Why do two different products trades as vol swap and var swap. Are these products not inter-convertible? I know Var swap has convexity and vol swap does not have but i don not understand how it helps in risk management. Can we calculate Vol of Vol if we know about vol swap and var swap? Is there any product like vol-var swap, i have seen this term being used?
I am starting to see the same question(s) posted thrice on three different fora sometimes. But to answer your question, volswaps and varswaps are two different products. I do not agree with your statement var swap has convexity and vol swap does not. It depends what your 'base' instrument is: if it is the varswap then the volswap has convexity, if it is the volswap then the varswap has convexity. I.e. convexity is a relative measure. No such thing as a vol-var-swap unless you mean a swap on the convexity correction, which I don't think you mean. Perhaps you've heard the term "the vol/var" before which is basically the basis between the vol and var, aka convexity correction. If you work under the assumption that varswap prices are lognormally distributed then given varswap and volswap prices you can say something about the vol of vol, it will be no different than the vol under Black-Scholes.
As mentioned by fomisha the volswap is model dependent. But: a large part of the volswap price is in fact model *independent*, even though there will be a relatively small model dependent component. There are straightforward ways to extract the model-independent part of the volswap price available out there.
When I say model-independent in this context I mean model-independent within the class of general (fractional) stochastic volatility models.