It's an interesting question indeed!
I think that the underlying methods/tools that are used in EDM
and LAK are probably similar. You develop models, programs and queries to mine through a large corpus of data to get some result.
I think that where EDM
and LAK are different is the intended audience of the data output. It seem to me that LAK is geared toward the educator and the team that the educator works with (principally instructional designers and educational specialists I'd say). LAK seems more classroom oriented.
on the other hand seems more like understanding students at the macro level (how they take courses, in what sequence, which courses are generally taken together, etc). I'd say that EDM
is more like the Google Latitude of learning analytics