Correct. Whatever amount of bitcoin you don't specify an output for will be consumed as a fee.

In the first transaction you linked, your input was 8000 sats and you only specified a single output of 2000 sats, so the remaining 6000 sats was used as a fee. If you did not want to spend all that on a fee, then you should have specified an additional output to a change address of say 5500 sats, leaving 500 sats unaccounted for which would have been taken as the fee.

Remember that if you try to send 2000 sats, bitcoin cannot "skim" 2000 sats from an available input. It must spend the entire input, and so you must specify a destination for all the coins in that input you do not wish to be spent as a fee.