These days, labels are used more casually than in the past. For me, the Perennial Garden is a move away from planting annuals or bedding plants. Done with that. I plant a few heat and drought tolerant annuals in containers, but very few now ... for the ground, I choose a few annuals that are heavy re-seeders and self-sowers or are easy to harvest the seeds for the following year (such as Hyacinth Bean Vine). And I plant lots and lots of wildflowers, tall ornamental grasses as well as shrubs that are native to my locale. A prairie, a glade, a bog, a woodland (especially at its edge), a meadow, a rock garden ... can all be cultivated to be Perennial Gardens. Right now I'm focusing on perennial vegetables.
I think the "traditional" Cottage Garden is rarely planted these days. Today's cottage gardens are much more informal. No hard and fast rules. They used to help provide a family's sustenance, but now it doesn't seem most people I know with cottage gardens plant the "food" part of it. Maybe some herbs or so forth. I always think of England, of course, when I think of traditional cottage gardens. The American Cottage Garden is something different. At least in my mind.
Great thread question, spring ... thanks for asking it.