The first difference is that while you are being taught, you are listening to someone explaining or telling you something new or something you don't know fully about, for example, a teacher. However, when you are learning something, it is not necessarily listening to someone teaching, but it might be something you read from a book or maybe from the internet, therefore you say "I learnt something from a YouTube video today" and not "I got taught by a YouTube video today".
Secondly, when you are taught by someone, you might not be absorbing or understanding the details that the person is conveying to you. This means that you might just be thinking of something else and not putting in your concentration and focus on processing the information that is passed on to you in your head. Learning something is almost the exact opposite. Learning means that you actually understand the details that you hear or see from the person, hence the expression "learning something new", whereby you know the procedure and understand the processes taking place within the information.
So, the next time you have to learn something for school or some other purpose, try to find the answers and information yourself first. There are many ways you can do this, from going to a library to searching for it on Google. Instead of always relying on someone to teach you about something, at least read up on the topic a little beforehand so that you have a better understanding of what the teacher, for example, is saying and also to cultivate some initiative in yourself.