The link to Department of State’s information:

Travel Alerts – According to DOS, these are short term/situational events that you should be aware of when traveling to another country. Examples they give include stuff like worker strikes or protests during an election, a disease outbreak, or elevated risk of terrorist attacks.

Travel Warnings  – These are more long term. DOS says this means you should consider very carefully if you want to make the trip to one of these countries. Examples include unstable governments, civil war, frequent terrorist attacks, sustained high levels of violence, etc.