Deriving those functions, you can find $p^*$ and $Q^*$, which, multiplying both, should give you equilibrium profits. Now, if you take that tax rate (20%, I reckon?), you can calculate taxes over profits and the tax-free price.
To find the equilibrium price $p^*$, you need to have those two functions in a system and solve for $p$. Then, just replace it on both functions and you should have equilibrium quantities.
Now, I'm assuming demand absorves all quantities produced by companies, no production restrictions and that this market is one in perfect competition. If this last paragraph changes, then my solution will not be correct.
To answer your question - what is the difference -, well, in this case, it is none because we are not considering production costs. If we did, you can see that both values would change.
Nevertheless, to calculate taxes, you need to work around with the system. That will give you total revenues, cost and tax free. Applying 20% leads to net earnings, because you do not have any production costs associated with the problem - something commonly done in Economics. That or consider a variable $c$ of costs.
This kind of exercises are also good to understand what are the effects of costs on revenues/profits. There's actually a financial term for that but I cannot recall :)
