With Doobie you manually write your queries, and then map the results into the objects in your domain model. Nothing is generated for you. OTOH, nothing is hidden and you are free to write queries as optimized and specialized as you need. The real selling point of Doobie is a typesafe API for manipulating and combining queries, and fragments of queries, into larger wholes. This works very well when your application interfaces with a database it doesn't own.
With Slick you get access to a DSL that lets you layout how your tables look. From there Slick offers an api that let's you treat SQL tables as-if they are basically mutable collections, with Slick handling all the SQL generation itself. You also get DDL, so that you can automate db creation and upgrades. This work very well when your application owns and controls the database it is connecting to.
Both of these have diverged from that traditional ORM model. Slick bills itself as FRM, or Functional Relational Mapping. And Doobie is embedded queries on steroids.