I think it depends on the resort. When we ate at Ohana a few years ago, we got a 3 hour parking permit (we were staying onsite). That is the only place I've ever gotten a parking permit. We've parked at CR for Chef Mickey many times and only had to show our KTTW cards and photo ID and we parked without any time limit. When not staying there, we've parked at ASMu, CSR, CBR, POR, and AKL without any time limits.
The official policy is that parking at a resort other than your own is limited to 3 hours. Now if the parks are not that busy, they may decide to not hassle you about it, or not even give you a parking pass.
They are usually the most strict about this at the Poly, the Contemporary, and at any Boardwalk resorts. Which does make sense as these are the resorts people would be the most liable to park at intending to go to the parks. Which is not what the resort parking lots are for.
If the guard doesn't hassle you about it or give you a parking pass, then don't worry. However if they do give you a parking pass you best abide by the time limit. Otherwise your car may end up towed.
I've been to WDW three times; each time we have had a breakfast at one of the monorail resorts, taken the monorail to MK, and come back at the end of the day. We have never been given a three hour parking pass at any resorts we've eaten at...Grand Floridian, Polynesian, Wilderness Lodge, the resort that hosts Yachtsman's Steakhouse. We always park in "visitor parking". I did not know that this was possibly not allowed...no one has ever told us otherwise, or given us a parking pass of any sort!
It really doesn't make sense to me that they would give you a time limit like that. What if you were going to visit your friend who was staying at that resort and you two were going to lounge around the hotel all day? Would they still give you a pass like this?