I am not well versed in this at all, and am going to beg that somebody notices my floundering to correct me and to better inform you, but let's give it a go! #DunningKruger :D
So Articulate Storyline has for a long time provided us a way to track users completing training using SCORM. Usually, that looks like a "completion" based on viewing so many slides or getting a score. You need the LMS to unpack that SCORM-reported data. If you don't have the LMS, a person might complete the training, but the trackable data doesn't go anywhere.
A growing practice is to put bits of JavaScript Object Notation (JSON) in an interactive training that leaves a trail of what behaviors the user took to complete a training. That JSON has 3 keys: actor, verb, object; and they combine to make an xAPI statement: "the actor acted on the acted". This statement is sent to an learning records store (LRS).
It is my understanding that many LMSs have an LRS built-in. Cornerstone has an LRS, so if I put an xAPI reporting course on Cornerstone, I can go to the LRS and see the actions a user took as they navigated a course. Meanwhile, I can still use my LMS to do all of those other things that the LMS does, like assign training.
Rumor has it that there is a way to provide a training without the LMS, and still be able to find the trail if you have the training linked to an LRS. I don't know where it goes. But still more rumor has it as possible to have person take a training at multiple locations, and route all of the behaviors from the various locations back to a single LRS.
The primary benefit of an LMS, as far as I understand, is the "management" of your learners. If you are training, but don't need to control the people, you could do with just an LRS... maybe.