Just for the sake of being clear and concise...
1: if you're staying at a Disney resort, you get a pass good for free parking at any of the parks, including the water parks.
2: if you want to visit a different resort, or have a meal there, when you arrive at the gate, you will, IN THEORY, be told you can park for three hours, maybe even be given a three hour pass. However, the actual enforcement of the three-hour window will vary, and again, IN THEORY, that three hour window is more of a big deal at the MK resorts and the Epcot resorts. WDW doesn't want a run of people using resort lots to avoid the ginormous lots for the theme parks, but the enforcement will depend a lot on how busy the resorts and the theme parks are. After all, if you're staying at a WDW resort, it's not like you're saving money by parking at the Poly and taking the monorail, as opposed to parking in the main lot and taking the monorail. I honestly have never heard of anyone getting towed for parking in a resort lot different from the resort where they're staying for too long. That's not to say it can't happen, or that it won't happen to you.
3: If you're NOT staying at a WDW resort and try to park in a resort lot, I'm going to make a rash assumption and say the odds are better that 3 hour window WILL apply to you, as it looks more like you're trying to avoid paying for parking.
4: Swan and Dolphin are not Disney resorts, so even with a WDW parking pass, you'll have to pay to park at those resorts. In fact I think even Swan and Dolphin guests have to pay for parking (or at least, they once used to have to pay, that may have stopped).
5: Nobody asked, but it comes up so: If you're a non-resort guest, and decide to park at the free lot at Downtown Disney and take a bus to one of the parks, be aware that none of the buses at DTD go directly to parks any more. You'll have to take a bus to a hotel, and then take a bus to a park from that hotel. OR walk to Saratoga Springs or Old Key West and jump on buses from there. Either way, you're taking a lot more time out of your day to save the parking fee. Hope you think it's worth it.