Sharing using a Copied Link versus folder.

Hi Janice, I'm a Sharing Product Manager here at Dropbox.  Just to build on Rich's advice here, I thought I'd add a bit more context for other folks who may come across your post.

Difference between "Copy Link" and "Share"?

Assuming you're referring to the options that appear when you hover over a file or folder in the browse screen, "Copy Link" is a shortcut to copy a shared link to the content based on your default sharing settings.  If a link does not already exist, clicking this will create a new link for you.  Share opens what we call the Share Modal - as pop up window which contains the full suite of sharing methods and settings.  From here you can either create shared links along with modifying their settings, or invite people to the content directly via email.  

Why does that person need to join my folder? Shouldn't they be able to access the files without joining?

Creating a view only link to content where link audience is set to anyone with link would not require someone to login to view.  You're correct there!  However view only folder links do offer recipients the option to "Join Folder" upon which they will need to login and would trigger a request access to you as the folder owner.  If you do not need recipients to download and don't want them to be able to join the folder, you can disable download and join from the link settings.

Hope this helps!