Yes, thats correct: The gray icon is a community lot, the purple one is a home lot.
The name “Community Lot” has nothing to do with the lot sizes. It means, your Sims can’t live there and when building and decorating houses on those lots, you can use certain items for free.
Both lots in your screenshot are Extra Large with the size of 54 x 36 squares. You can only build houses there, that fit in 54 x 36 squares.
The Duketon University has 18 x 36 squares, so it doesn’t fit in 54 x 36 squares. You can build it on any “Ocean View Residence” in your town. It doesn’t have to be built on a Community Lot. If you want to build it on one, you can only use the Barter Boardwalk lot.