Yo do not need to have premium to pay for league fees, though you do have to be premiumed up before the server is assigned for your match or something. You pay for league fees by clicking on the "League" tab and clicking "Register and Pay." You pay for premium by clicking Play Now, but you have it until December 1st, which means that most likely your premium will expire a few days after December 1st, unless you have your premium on paypal subscription or something similar. Yes, league fees are the fees you pay to register and play officially in IM / Open, etc. Premium is used to play in pugs, use the other features of esea, and is one of the other steps to playing in a match.
To summarize: No they are not the same thing; you can just pay league fees for now, but must be premium to play a match.