What constitutes a project to be a Bitcoin Sidechain? From my understanding sidechains require the parent blockchain (bitcoin) to be able to lock a certain amount of coins on the sidechain. My question is how is it different from just sending your btc coins to a 3rd party and they just hold it while they give u their own tokens to play with. How is coinbase different from rootstock which is supposedly a sidechain right? I know coinbase is a company that holds your btc, but doesnt rootstock also hold your btc? The thing is how do they hold it?
A sidechain requires one or more blockchains, aside from the parent chain. This is different from off-chain, which is what would be the case in some types of Coinbase transactions. Since you didn't mention the presence of an additional blockchain in your other reference to a 3rd party which provides tokens in exchange for a payment, I would assume (albeit subjectively) that it would probably be an off-chain type of transaction in that example, too.

Rootstock, on the other hand, has its own blockchain, to create a 2-way peg with Bitcoin to facilitate smart contracts and other potential features, like near-instant payments.

Here's more information about sidechains in case you'd like to read about them in more detail. There are additional technical components beyond the presence of one or more blockchains:


Enabling Blockchain Innovations with Pegged Sidechains
A Simple Explanation of Bitcoin "Sidechains"