Column-based and column-oriented are essentially the same thing. Essentially, data for specific columns is stored together to make querying that data faster, as well as scalable. Examples of columnar DBMS products are: Druid, MonetDB, and Vertica.
In terms of how Cassandra relates, the answer to that is that it doesn't. Cassandra is a partitioned row-store. Column values are stored by partitions and rows.
You are not alone in this perception, as many people mistake Cassandra for a "columnar" data store. Earlier versions of Cassandra were considered "schemaless," so that may be where some of the confusion originates. But Cassandra has never embraced a storage model which keeps data for specific columns together.