row-oriented

A relational database stores data in rows and reads data row by row.

sql

The oldest and most well known type of relational database. SQL is a strange beast. I don't even think it's accurate to call it a standard as each implementation varies significantly from the rest and none of them implement the so called "official" standard. SQL has survived in spite of itself because the idea of a relational database is just that useful.

column-oriented

A type of database that stores data on disk in columns instead of rows. The purpose of a columnar database is to efficiently read data from hard disk storage in order to speed up the time it takes to return a query.

Unfortunately there is no free lunch, which means that while columnar databases are great for analytics, the way in which they write data makes it very difficult for them to be strongly consistent as writes of all the columns require multiple write events on disk. Traditional row-based relational databases don't suffer from this problem as row data is written contiguously to disk.