Do you run a node in pool while you stake in a pool?

I have went though several videos, FAQ’s and threads but I always come out a little confused. When you stake in a pool; do you need to run a node within that pool or is it just the owner / organizer of the pool running the node? I guess another question would be how many nodes are expected in a pool? Reading everything from the Cardano FAQ’s makes it seem like you do not need much to have a node compared to mining. I guess the better question is does the staking pools function like mining pools as in everyone can run a node and the split the rewards… Thanks in advance!

Here’s how I understand it.
A staking pool is one node. (I don’t know if it’s possible to even run multiple nodes in one pool) The pool owner runs the node. People delegate their stakes to that pool to participate in the block creation process and also to earn rewards.
Stake delegators don’t need to run a node, they are simply assigning which staking pool their ADA goes to. This is planned to be done on ADA wallets. The pool owner doesn’t need to own a large amount of ADA. They can create a pool with 1 ADA and let other people add into that pool.
Rewards are split proportionally based on the ADA each participant staked. However, the pool owner gets a higher reward percentage for running the node as to compensate their effort in maintaining the pool.

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Thanks I figured as much but some of teh wording is kinda vague.