I am afraid, Just, that a lot of "definitions" with regard to computer technologies tend towards the fluid. An SMS, for me, has a number of student oriented functions that do not appear in Moodle. On the other hand, the SMS tools I am familiar with do not have much of the functionality that Moodle does, except Blackboard. (If file handling were to be excluded, then I doubt there would be any common functionality.) The Wikipedia article could have been written by the PR dept of BB, as that is the only tool I know that comes close to meeting all those criteria, depending on how one would interpret what the criteria in the terms of definition mean.
And I should have thought of ELIS myself, yes, a handy set of tools there, quite right.