What exactly is the relationship between SideChains and main chain?

I am trying to understand sidechains and how they relate to ethereum but all the articles I read keep saying things like:

A sidechain is a separate blockchain that runs independent of Ethereum and is connected to Ethereum Mainnet by a two-way bridge

That is from here

But I don't get it. Solana has bridges to Ethereum, does that make Solana a side chain of Ethereum? Polkadot has bridges to Ethereum, is that also a side chain?

I mean what makes an ethereum "sidechain" distinct from other "chains" that can also have bridges to Ethereum?

Also in the article above, it is stated that:

Sidechains can have separate block parameters and consensus algorithms, which are often designed for efficient processing of transactions

Okay so sidechains have some edge over mainchain, mainly processing speed. If that is the case, why then does it need to be connected to the mainchain and acts as a sidechain to the main chain?

I ask because it is also stated that the sidechain does not derives it's security from the mainchain. So if it does not derive its security from the ethereum mainchain, why does it then even have to have a "sidechain relationship" with the ethereum mainchain.

Can someone please help explain? Thanks