Can You Have Both Anorexia and Bulimia?

Can you have bulimia and anorexia at the same time? I really don’t know what to call my eating disorder. It definitely started out as anorexia and then later I started to purge the little bit that I did eat. Every once in awhile I’ll binge, but it’s not like the 2000+ calorie binges that are usually associated with bulimia. I would eat a little bit of a lot of things, pretty much anything I could get my hands on. But I would only eat a tiny bit of each thing. I could down a whole new bag of grapes but I just chewed them up and spit them out and then purged the grape juice along with the other food I snacked on. Now I really don’t eat much anymore, but what I do eat, I throw it up. I’m terrified of eating anything one minute, and the next I can eat cheezits no problem, but not a salad at dinner. It’s so confusing. It’s like I’ll order a ton of food, but only eat a little bit of each thing and then purge it. Is this anorexia? Is this bulimia? Is it both? Is this something else? I feel invalidated because I don’t know how to correctly name what’s wrong with me. I can’t relate to ppl with anorexia all the time, neither can I relate to ppl with bulimia all the time. I don’t know what to do and I feel like no one takes me seriously.