Salary cap - $$ amount set by NBA that severly hampers a teams ablity to sign/trade new players, but with a savy GM deals can get done. $49.5mil
Lux tax - the hard cap that when a team goes over it they pay a $ for $ amount that exceeds the $61mil it's set at. For example the Mavs have a $95mil payroll which means they're paying roughly $34mil in tax. The tax $$'s collected are then divided up and given to the teams UNDER the lux tax.
Vet mins, i believe, still exist but i don't know what the amount is. The MLE and LLE are given to teams(all teams?) with little salary cap flexability so they can sign players. I'm not sure how they effect the lux tax though.
The new Amnesty clause allows a team to dump a high contract player and remove their salary from the lux tax. BUT it still counts against the salary cap. Example, Finley. He's owed $51mil remaining on his contract. By releasing him the Mavs save $51mil in lux tax over 3 years, BUT he still counts against the salary cap.
Somewhere there is a site that explains it; maybe someone has it bookmarked.
HTH

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