A fee rate is the fee a transaction pays divided by the block space it takes. The fee is what its inputs hold minus what its outputs pay, in satoshis; the space is its virtual size in vbytes. A block holds at most four million weight units, a million vbytes, so a miner filling one earns most by taking the transactions that pay most per vbyte.
That is why the Network tab prints fees as sat/vB and never as an amount per transaction. The same fee rate costs a one-input payment and a hundred-input consolidation very different totals.
The figures on the desk are one node's view. mempool.space estimates the rate that would clear in the next block from the transactions its node holds; another node, with another mempool, could estimate differently, and no estimate is a quote.