혼자 and 홀로 as an adverb both have same meaning of "alone, (all) by oneself, (all) on one's own".
혼자 is mostly used colloquially. 홀로 is used for a literary style sentence.
Also, 혼자 can be used as a noun.
ex)
그녀는 아직 혼자다
She is still unmarried.
이건 혼자만 알고 계세요
Please keep this to yourself.