PM (meaning "private message") is sent through BYC and will appear in your message box. Click on the "Messages" link at the blue bar at the top of the screen.
Emails are sent directly to your email address. If you don't want people emailing you, you can change the settings for that under your profile.
Most folks on BYC use PMs unless the person requests emails instead in their posts.
A PM can be accessed here on this site - ...whereas if you hit the button to email someone- the message will go to the persons actual email adress they have used to register with the site.