Differences between Lightsail integrated database and managed database?

Hi.

When installing a database on an instance, all maintenance such as updates and backups must be managed by the user.
In the case of managed databases, Lightsail's managed features provide this convenience.
A managed database is a good choice for high-availability systems. (However, in that case, it is better to consider services other than Lightsail such as EC2 and RDS)

The Lightsail WordPress template installs the database within the same server.
If you choose WordPress yourself, you can choose to connect to a managed database, but it is not required.

Agree with @iwasa. The two biggest differences are that the managed database is updated and maintained FOR you whereas an instance database is managed BY you. The second is that with a managed database you are essentially freeing up resources on your instance for activities and usage of your webpage/WordPress whereas when they share an instance, they are essentially competing for the same resources. You generally will get higher performance with a greater traffic load when running the two independent.

Even though I say this here, most of my WordPress blogs run on the same instance just fine. I use the medium ($20/month) instance