Notifications are single at-a-point-in-time message. This may be sent via in-app notification, system notification or email. Different communications channels are used for different message types, often for regulatory reasons.
Although notifications cover many message types, included within this are notifications relating to any nudges if you choose to set a nudge up.
A nudge is simply a standing instruction on how you would like to be reminded on something (e.g. a reminder to save on the 1st of the month). Whenever the nudge criteria are met on an on-going basis, a notification will be sent.