On the pattypan vs. sunburst squash issue, it's a tricky one. The answer to your question of whether that's a pattypan or sunburst in your crisper is, "Yes."
Here's what my convoluted Internet trail-blazing led me to: The sunburst squash is a kind of pattypan, pattypan being marked by its flying-saucer shape with scalloped edges and sunburst being a yellow variety of pattypan.
Dictionary.com's entry for pattypan identifies the pattypan's color as white, or greenish-white. If you want a more official aggie site, the UK's Royal Horticultural Society calls the sunburst the best variety of "Patty Pan" (they separate the two words, but I think they're kind of jolly squished together and in all lower-case letters). Also, they associate the pattypan with winter squash, which is perplexing:
My last source, The Cook's Thesaurus, lists pattypan (one word!) as part of the family of summer squash. Summer squash is distinguished from winter by the fact that you can eat it entire, seeds, rind, and all. I think I'll side with the Cook's Thesaurus over those British blue-bloods on calling the pattypan a summer squash. They also give a nod to the sunburst, "There are green and yellow varieties; yellow ones are sometimes called sunburst squash.""The Patty Pan types of winter squash, all of which can be left to develop and mature for winter storage, seemed to work particularly well when harvested young. The fruits are not unlike flying saucers with flat, round fruits and wavy edges. Undoubtedly the best of these was the cultivar ‘Sunburst’ which produced many small, bright yellow fruits."
I first heard the term "pattypan" from The Naked Chef, Jamie Oliver. He uses them in a delicious Food Network recipe for couscous with grilled summer vegetables that I like to make for potlucks or big groups of people.
[Insert cringe-worthy pun involving "squash" here, i.e. "I hope I squashed that question," or "Sure ran that one through the squashing machine," etc.]