You pay when you get there
If I understand your question correctly, when traveling to Logan you want to purchase your tickets in advance, because they're are cheaper. As for parking you will pay before you leave they have kiosk in the lobby. The rate is cheaper than parking at Logan and you don't have to fight the traffic.
If you pay online you get a discount of $4 so it's better if you pay online because it's $8 or $9 a head and it's 12 in the facility
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