Amazon has a ton of options for databases. But the three most common ones that you may come across are DynamoDB, DocumentDB, and RDS.
DynamoDB is a fully managed service. This comes at the cost of flexibility.
DocumentDB is basically a MongoDB NoSQL database. It's more flexible than DynamoDB but requires more management from you.
RDS stands for Relational Database Service and it is probably the most familiar to the majority of us. You can select from database engines such as PotgreSQL, MySQL, Oracle, and amazon's Aurora.