Some questions about MEV, PBS and MEV-Boost

After reading this page from Ethereum.org, I have some questions and thought you could help me understand it better. I put my own understanding but please tell me if I'm wrong or what I'm missing.

Thanks!

1. What's the difference between PBS (Proposer-Builder Separation) and MEV-Boost?

PBS:

• PBS design is still in discussion.
• PBS would be implemented at the protocol level, meaning it will be built in Ethereum consensus protocol and would change the way blocks are built and proposed for every Validator.
• PBS design doesn't rely on third-party Relayers

MEV-Boost (from Flashbots):

• Use the same idea of PBS: separating block Builders and block Proposers
• is a client that Validators can install in order to access a some kind of "auctions market" for MEV-optimized blocks.
• The Validator becomes a Proposer. By calling the Relayer (via MEV-Boost API), this Proposer selects the most profitable block, among blocks built by Builders. Those Builders want their block to be included because they want to extract MEV, so offer high gas fees (some kind of "profit sharing" between the Proposer and the Builder).
• This is somewhat centralized because the Relayer is a third-party (unlike in true built-in PBS). But still better than nothing because without MEV-Boost, there would be less competition and more centralization risk (Searchers would be frontrunned by Proposers ; Searchers / Builders would make private arrangements with the biggest Validators/Pools).

Am I right or did I miss something?

2. Are Searchers and Builders actually the same actors?

• The Searchers are the actors that look for MEV opportunities ;
• Builders are the actors that actually build the blocks and bid for its inclusion (via a Relayer in the case of MEV-Boost) ;
• But I suppose Searchers build blocks themseleves (just because they can and I don't know why they would delegate this to someone else).

Am I right?

3. With MEV-Boost, what does prevent the Proposer to frontrun the Searchers?