A conflict is something general or ongoing. For example, there is a lot of conflict in the Middle East. Clash is a disagreement, often violent, between two opposing groups or individuals. Clash can also describe the low noise of things hitting eachother. Pans hit together make a clashing sound.

They are synonyms. It would be best to check a dictionary to see which one is more appropriate for you. Try this one: https://dictionary.cambridge.org/dictionary/english/clash https://dictionary.cambridge.org/dictionary/english/conflict You could also use a collocations dictionary to see which word goes best with the other words you will use with it: https://www.freecollocation.com/search?word=conflict https://www.freecollocation.com/search?word=clash

Like Christina said. the word can have different meaning. I'd like to add another situation where the word is used to give a different meaning. If colors or styles don't match and look ugly or wrong together, you can use this word. "The red and orange stripes in her shirt clash with her blue jeans."

Clash is more colloquial and conflict is more formal.