What is hyperdrive and how is that different from dat?

TL;DR: Dat is for end users and Hyperdrive for developers.

Dat is a user friendly interface for sharing distributed files. Anyone can download the program and use it to securely share files peer-to-peer.

Under the hood it uses Hyperdrive which is a Node.js package that aims to implement the same APIs as Node.js' core fs module, but it also offers data replication features.

There also is a dat-node module to use Dat's features in your own Node.js applications. With dat-node it is even easier than with Hyperdrive (just a little less flexible) to connect your own Node.js application to the distributed network.

If you compare the documentation of Hyperdrive and dat-node you'll quickly spot the simplified interface which dat-node provides.