tomcat publish/clean/remove

publish:

"Publishing", they kind of mean "Deploying", or "Copying to the deploy directory", depending on what server you are using.

from stackoverflow

deploy

http://localhost:8080/sample

Deploying of wars is automatic by default

clean 

Clean: Purges all webapps and redeploys them (don't do this while the Tomcat instance is running)

Clean working dir: Cleans out Tomcat's work dir, e.g. where compiled JSPs go.

http://www.coderanch.com/t/87174/Tomcat/Purpose-work-directory-Tomcat

remove