And Thomas Keller cooks. What's your point?
It seems to me that this thread has strayed very far away from what the OP asked and for very little actual purpose -- other than to say some consider themselves better a housewife who is known for a few particular dishes which she takes to potlucks. Otherwise, the big takeaway is that the better you cook, the better technique you have, and the better range of dishes which means the less likely you are to have a particular specialty.
"Chef" is a word, not a state of grace. It's definition was not written with a flaming finger on a stone lintel, but -- like any definition -- is created by usage.
I don't cook professionally anymore, but I worked on the line in very good fine-dining kitchens for a few years, and had a fine-dining catering company for a few more. Even though I have solid technique, and do a lot of things very well thank you, I'm better at doing some things than others, and that's probably true for most professional chefs as well.
If you cook Mexican cuisine equally as well as you cook French, Indian, Chinese, Greek and Cajun, you might be tremendously flexible, but it's far more likely you're not that great at any of them.
I joked about desserts but it's true that I don't have the interest, the skills, the flair for presentation, etc., that make for a good pastry chef (or pastry cook, if you will). I can do a good job on a few items, but don't have much of a repertoire nor much ability to vamp. Maybe those few things are specialties.
My strengths are hot pan, grill, "Q," saucing, and -- perhaps -- bread making. My interests in particular dishes and styles constantly evolves, although my so-called "culinary viewpoint" has remained constant since Moses wore shorts. I'm "ingredient driven," which means I usually try to highlight certain ingredient in each dish and on each plate and use a combination of palate, technique, and other ingredients to enhance the "stars" so they taste very much what they are.
My catering business was a lot like what people now call "personal chef," I had a stable, limited clientele, and usually did small groups (lunch and dinner parties) as opposed to big events (hate them). My clients had their favorite dishes from my repertoire. Maybe those were my specialties.
For the past few years, my primary interest has been "retro" and regional American. I think I do "California Barbecue" as well as anyone -- pro or home -- so maybe that's my specialty.
If I went to a lot of potlucks, I'd probably end up mostly bringing the same things both because they were well received and expected, and because they went well in potlucks. Maybe those are my specialties.