Forge helps you build and manage servers with all the necessary software that most Laravel apps require (web server, database, redis, etc). It has a basic deploy feature, but there is going to be some downtime when pushing new code up to your production app. It can be anywhere from a few seconds to minutes, depending on the size of your app.
Envoyer is a tool that allows for no downtime when deploying. It's not specific to Laravel apps.
They have features that integrate nicely with one another, but both are not required.
I personally use both and love them. For any "real" apps that have actual users, I use Envoyer. For any demo projects, I just use Forge.