Sidechains refers to blockchain interoperability, that is, for one blockchain to be aware of another's state. This would allow for "transfer" of tokens from say BTC to a "sidechain".
A sidechain here simply means another blockchain by the way. The way a token could be moved is by freezing it on one chain and minting it on the other, then to send back, freezing/destroying the token and remobilizing the original coins.

Treechains are a different way of organising and mining a blockchain such that you dont need mining pools. Treechains can utilise sidechains. There is no competition per se, except that sidechains, as currently proposed exacerbate mining centralization.

There is good stuff in sidechains, but it does not remotely solve bitcoin's scalability issues while treechains does. There is good tech and ideas in the sidechains concepts and I am sure treechains will incorporate some of those. Token transfer for example would be possible with treechains.