"I learn English."
I would say that studying is a mix of learning and intensely revising what you have learnt for memorisation/to retain what you have learnt. Study is often something that is done by yourself (although you can study in groups with varying degrees of success - my best friend and I could never study together because we would get distracted looking up funny words in thesaurus' and talking etc) and which requires personal discipline and dedication. Learning can be done by yourself or in a group - I would say that it is a process of familiarising yourself with new skills, knowledge and techniques etc - you can learn new things and add to or improve the skills and knowledge that you already have. Both learning and studying describe ongoing processes but studying is usually going over things you have learnt or in other words the process of making sure that you remember and keep current the things that you have learnt. Hope this makes sense.
It's definitely learn - check the kanji 学びます、学校、学者 - manabimasu (to learn), gakkou (school), gakusha (someone who is learned or in other words a scholar). - just editing this as it was in answer to your original comment which you've since edited. Your comment now seems more in line with my own experience of these two verbs. When you learn something from someone it is ni narau - an uncommon usage of ni where it means from eg. haha ni narau - I learn from (or by) my Mum. Both the from and the by sound odd/unnatural in English but they are helpful for explaining what the ni is there for in the Japanese even if you don't include that in your translation. Another instance where ni is used like this is with morau (to receive) tomodachi ni tsukutte moraimashita - I had my friend make it for me - but literally I received the making of it/something from my friend - or something like that.