I understand they both translate to meaning, "to learn, to study" but what is the purpose of this distinction?
There are still a lot of differences in between I think.
- For most cases, when you want a verb meaning "to learn", either of them can be used. Only xuexi is having more syllables to make you sounds more formal and polite.
- When used as a noun, xuexi is more frequently to be used to express "learning".
- Also, xue has more meanings rather than "to learn" as a verb. It also means "to imitate", "to perform as"-e.g. shuoxuedouchang（说学逗唱）
xuéxí 学习 Study
xué 学 Learn
习 carry the meaning of "practice". So 学习 = Learn and practice.
You can acquire the meaning from dictionary.com
Study : the devotion of time and attention to gaining knowledge of an academic subject, especially by means of books.
Learn : gain or acquire knowledge of or skill in (something) by study, experience, or being taught.