I think it is fabulous that the teacher is noticing things, talking to you about her observations and trying to come up with ways to help your daughter. The teacher is most likely not qualified to make a diagnosis, but it is very possible she has seen this before and has worked with similar students. So her observations are relevant, but you will need a specialist to make an official diagnosis.
We are going through the IEP process with our kindergartener, so I am by no means an expert. I do hear people throw around the terms IEP and 504 plan, and this website does a nice job of explaining the difference:
https://www.understood.org/en/school-learning/special-ser...
Both of these terms are backed by Federal Laws, so they do not vary from state to state.
I would talk to your pediatrician AND ask the school for an evaluation. The ped will be able to refer you to the appropriate specialist. That's important! In order for your daughter to have an IEP (or even a 504 Plan) the school will need to do its own evaluation. Save yourself some time (and these things do take so much time!) and just start the ball rolling on both!
Right now, it's less important for you to learn about dyslexia, processing disorders and other similar diagnosis, because you're not the one who can diagnose her. The best thing you can do is find out who the appropriate specialist is and take your daughter there.
When our son’s psychologist offered a diagnosis and explained it to us (he hit the nail on the head, by the way) I had a deeper appreciation for the depth of his knowledge and experience. He was diagnosed with Social Pragmatic Communicative Disorder. Tell me you've heard that one before. Yep, never heard it myself! His teacher and the principal hadn't either. There are many things we have heard of – dyslexia, sensory issues, autism – there are many, many things we have not heard of. Your daughter could very possible have something you’ve never heard of. That’s why you need to talk to someone who actually is qualified to evaluate and diagnose.