The grocery store can be a confusing place. It's all about product placement, but just because items are next to each other doesn't mean they are the same. Take eggs for example. They are generally in the dairy case and people ask me all of the time if eggs are dairy products.
The short answer is no. They should be refrigerated, which is probably why they are located near the dairy case. Dairy products also need to be refrigerated. So, I get why some folks are confused.
Cows have a few different purposes, but I've yet to see one lay an egg. Dairy cows produce milk and at the end of their lifetime, meat. Beef cows just produce meat.
Eggs and dairy are both great sources of protein. For a recipe that involves both, check out my Cascade Scramble. It's SO good!