The main difference is that a teacher should be able to teach you the language, therefore italki has some requirements:
- Professional teachers have training as educators and/or extensive professional teaching experience. They can provide students with resources, prepared materials, and structured lesson plans to help students reach their goals.
- To apply for a professional teaching profile, you must upload documents showing your training and experience as an educator.
- "Native" or Advanced (C2) language proficiency
While a language exchange partner can be anyone that has some knowledge of the language you want to learn:
Language Exchange is when you find a language partner who has complementary language skills to you.
Language exchanges are free and very informal. You and your language exchange partner are simply exchanging time and helping each other learn your respective languages.
The idea with the language exchange is that you practice with another person that speaks the language you want to learn better (for example being its native language).
I would conclude that both can help you, but if you want to get more knowledge about a language a teacher can help you more. However, a language exchange partner is really useful to get more fluent in a language, and obviously by that you will also learn; furthermore they are cheaper since there are several places where you can do language exchange for free.