Set an email/thread to "Notify me". Go to Settings > Notifications > Mail. You should see this list:
Exchange
iCloud
VIP
Thread Notifications
The top two let you set up the notification style for Exchange and iCloud emails, and then you can override those settings for emails from VIPs and for emails set to notify you.
The term "notify me" is pretty poor, because theoretically you could set it up to show less notification than the defaults for Exchange and iCloud! (I'm someone who has banners and lockscreen set up for all emails, I don't personally have much use for this new option. At best I could make it play a different sound)
So to answer you question, the difference is whatever you decide it to be. By default the difference is that you get a banner and it shows on the lock screen, which doesn't happen for normal emails.
Sorry if I've missed the meaning of your questions again!