Ha! I can out-pædant anyone here!
Tomcat is, according to generally-accepted usage, a Web Application Server.
Tomcat is - in a limited scope - a J2EE web application server. It is not, however, a full-stack web application server because it lacks several of the heavyweight capabilities (such as EJB container) that are required to be provided in order to be certifiable. Tomcat only provides the servlet/JSP support, a JNDI server, Database connection pools, security Realms, and a few odds and ends.
Despite Tomcat's limited capabilities, it has served as a prototyping platform for next-generation servlet/JSP designs. It also has been employed as the servlet/JSP subsystem services provider running embedded in full-stack J2EE/JEE web application servers such as JOnAS and
JBoss,
----
So much for nit-picking. In Tomcat versions 6 and greater, the database driver JAR must be copied into the TOMCAT_HOME/lib directory. It must NOT be included as part of any application (WAR) because it's used at the container level by the connection pooler(s) and individual application classpaths are not shared as part of the server classpath. The server's classpath is part of the individual webapp classpaths, though.