Moving my blog to a new server

Per the Codex, Backing Up Your Database using PHPmyadmin, I’ve got my backup in sql and sql.zip file.

Next, it says, “Remember – you have NOT backed up the files and folders.” In the Codex, Moving To Another Server, the first step is “Download your complete WordPress installation and any other files that are needed (such as images).” Is this what’s meant by “backing up all files and folders — and do I do this with my ftp?”

The final instruction is, “Now check that you really have backed everything up.” Does this just mean looking at their name & size on my hard drive, or is there another, better way to confirm?

Thanks.