The synonym of “differently” is “variously”.
Both words convey the idea of not being the same or in a particular way that is distinct from others. For example, “She approaches problems differently.” could also be expressed as “She approaches problems variously.”
Another synonym is “diversely”. This also implies a sense of variety and difference. “The city is populated diversely.” is similar in meaning to “The city is populated differently.”
“unlike” can also be considered a partial synonym in some contexts. For instance, “He acts unlike others.” means he acts differently. However, it is more limited in usage compared to “differently” or “variously”.
“distinctly” can also sometimes be a synonym, especially when emphasizing a clear difference. “He sees the situation distinctly.” can imply he sees it differently from others.
In conclusion, words like “variously”, “diversely”, “unlike” and “distinctly” can be used as synonyms for “differently” depending on the context and the specific nuance one wants to convey.