I paid this dude $20 usd for a $13.75 usd mining fee. He said it would take 2 hours. It has been 24 hours. I look in the transaction details and discover he only paid just over $3 usd.
I really wonder why and who this guy is that you paid
Checking your other thread
https://bitcointalksearch.org/topic/m.26004670
Somebody tricked you and lied to you.
It would be better that you publish their name/account/website/localbitcoin account or whatever they are so other don't get tricked.
Again, you're confusing the miner's fee and a transaction fee. The miner's fee (as named) is charged by the miner for confirming the transaction on the blockchain. A transaction fee could be charged by the exchange the two parties are using to facilitate the transaction. It's likely to be two different exchanges for one transaction (one for the sender, and a different one for the receiver). And both exchanges are likely to charge a fee to pay for the service they're providing to either party.
Some exchanges will combine the miner's fee and the transaction fee so the sender or receiver just sees one line item labeled "transaction fee".
Actually he is right.
A tx fee is always payed to the miner. It is not charged ( as there is no price label on it) it is offered by the sender and (maybe) accepted, it is not set in stone and not enforced by one of the two.
The other fees are not related to the tx.
Those are service fees for withdraw or deposits and are set by the service provider and agreed in the ToS.