1. Saya mau belajar Bahasa Indonesia.
2. Saya ingin belajar Bahasa Indonesia.
Well they quite have the same meaning, but slightly tell a different message. In this context, the 1st one could mean "I'm willing to learn Indonesian language" (if you use "mau" as formal) or "I'm going to/I want to learn Indonesian language" (if you use "mau" as informal, but in informal we never use "saya", we use "aku" instead), while the 2nd simply means "I want to learn Indonesian language."
However, "mau" is widely used in colloquial indonesian, while "ingin" sounds too formal ("pingin" or "kepingin" is the informal way of saying "ingin"). Sometimes they can be used interchangeably, but not always. To make it less confusing, "ingin" will always mean "want" and anything related to it, while "mau" can be interpreted in several meanings.
In informal context:
mau+verb means either "want to do something" or "going to do something"
mau+noun means "want"
Example:
-Mau kemana? (Where are you going?/where do u want to go?) << you can omit the subject "kamu" when talking directly to the person
-Aku mau makan. (I'm going to eat/i want to eat.)
-Mau makan apa? (What do you want to eat?/what are you going to eat?)
-Aku mau nasi. (I want rice)
In formal context, "mau" is normally used to express one's will, so it cannot be combined with just random verb.
-Saya mau belajar! (I'm willing to learn!)
-Saya mau berubah! (I'm willing to change!); Saya ingin berubah! (I want to change!) << can u feel the difference? :)
Sorry for the super long explanation, im not a language expert but that's my point of view as indonesian. I hope it helps and goodluck! :)