It means different things to different people I've seen.

Most of the time when people explicitly say they want a "Front-end Web Developer" they want someone who is good with all the front end code (html, css, javascript, <insert scripting language>)

They would like it if you can design but its not necessary.

More often I've seen people who say "Web Developer" or even "Web Designer" really want someone who can do both web devel and design

This often frustrated me because I can code but couldn't design my way out of a paper bag yet.