BookBaby is a printer and publishing services entity. It also has its own bookshop, but the shop won’t have the reach of Ingram or Amazon. It will also distribute to them and everyone, basically, but the price for that service is high. I used them only for printing copies for myself to sell directly; I didn’t opt for distribution. I also did not try to make an ebook with them; I’m getting the impression that KDP will continue to be the best bet for ebooks.
If you do choose BookBaby, it will likely be because their print quality is a bit higher than others, because they have a great quote system for figuring out what you want for your book, and because they will also actually talk to you on the phone about your quote, etc. Their customer service is stellar.
Keep in mind, though, that they do have wider margin requirements for their book layouts than either Ingram Spark or Amazon, which means that they are by definition more expensive to print since with wider margins, you will have more pages (unless you reduce your text size).
PS: You can also submit your book to more than one printing/distribution company. Here’s an article on the advantages of submitting to Amazon KDP and Ingram Spark for the same book.