In Ubuntu I normally install both but what are the differences between the client and server for MySQL.
As a bonus, when a new statement mentions that it needs MySQL 5.
MySql Client :
The mysql-client package allows you to connect to a MySQL server. It will give you the "mysql" command-line program.
MySql Server :
The mysql-server package allows to run a MySQL server which can host multiple databases and process queries on those databases.
MySQL :
The "MySQL" package probably includes both of the above.
If you just need to connect to a remote server and run queries, install just mysql-client. If you need to host a database, install the client and server.