Something that's swampy is very wet and soggy, like a swampy baseball field after four days of heavy rain.
Something swampy resembles a swamp, a wetland where trees, shrubs, and other plants grow. The "wetland" part is what's important when it comes to this adjective, which you can use for sloppy, squishy places that get your feet really wet. That park won't work for croquet — the grass is so swampy! Swampy can also describe literal swamps: "Cypress trees grow in the swampy areas of Louisiana bordering the Mississippi River."