An LMS is the abbreviation for Learning Management System.
This is software created to manage elearning courses, classroom courses and learners.
It will deliver and track the completion of those courses and allow you to report on learner activity.
elearning is essentially learning that is conducted via electronic media and typically done over the internet by using a computer or other internet enabled device.
It is training that can be completed at your own pace and outside of the classroom environment.
SCORM (Shareable Content Object Reference Model) is an internationally recognised standard for tracking elearning usage.
xAPI (aka Tin Can) is a new specification that allows learning content and systems to communicate to record all types of learning experiences, not just elearning.