“Aloud” tends to be used in more formal speech, and was the preferred form in usage guides in the early 20th century. “Out loud” was considered the colloquial version of “aloud.” You’ll find “aloud” used more often in sermons and academic papers, as well as books scanned by Google. It’s common in sentences such as “The passage was read aloud in church” or “The letter will be read aloud at the press conference.”
“Out loud” is used more often in informal writing and social media posts, and is found more frequently than “aloud” in Reddit comments. It’s also used more than “aloud” in certain contexts, such as expressing shock that something was said: “I can’t believe I said that out loud.” You’ll also hear “I was thinking out loud,” or the demand “Say it out loud.”
Either “aloud” and “out loud” are acceptable in any format, so use whichever one feels more natural to you. But if you’re a fiend for good grammar, stick with “aloud” in more formal speech and writing, and save “out loud” for the more relaxed writing.