yes, the kanji has the meaning you mentioned: 'manabu' means 'study'. the word 'manabu' is noun and verb. 日本語を学ぶ (I study Japanese) manabu is used as verb. 学ぶことは楽しい (studies are fun) the word, 学ぶ, cannot be read as べんきょう. べんきょう is a noun. にほんごをべんきょうする (I study Japanese)

Basically, まなぶ means "aprender" and べんきょうする means "estudiar" but in my opinion, there are differences between in the Western languages and in Japanese. We use べんきょうする for "aprender língua(s)" and "estudiar língua(s)" in general. Besides, we sometimes use other translation for "aprender" like "memorizar", for example, I would say "aprender 10 kanji" as "memorizar 10 kanji" when I say it in Japanese. We have to try to use the most appropriate one depending on the situations to make it more natural, however, all are understandable. I hope this was helpful. Muita sorte to your Japanese.