While both are templates more than specific "Do exactly this" type programs, TM usually refers to somewhat more specific guidelines than HLM. The basic idea of TM revolves around a higher volume/medium intensity day at the start of the week, a lower volume and lower intensity day mid-week, and a lower volume/high intensity day at the end of the week; and in its most basic form, you hit a PR for the prescribed # of reps on that end-of-week Intensity Day.
Whereas HLM is a much more general template that can be used with a very large variety of set and rep ranges, along with a variety of scheduled "planned PRs."
Things get a little messy, however, because you can also easily adopt the basic TM ideas and structure for longer periods, too. Comrade Campitelli and I have discussed a version he has used with his lifter Mune - who has competed nationally and internationally in the IPF - wherein Week 1 is Volume Week (with a tiny bit of intensity to preserve the skill), and Week 2 is Intensity Week (with a dash of volume to not totally detrain on it before returning to higher volume the following week).
I've personally played with TM-based templates that keep the basic TM structure of High Volume/Medium Intensity, Low Volume/Low Intensity, Low Volume/High Intensity but jigger it to aim for a PR every second Friday.
i.e. for a lifter whose 5RM is 405, 3RM is 430, 2RM is 450 and 1RM is 470:
W1D1: 375x5x5 - hard volume day
W1D2: 275x5x2 - very easy light day
W1D3: 410x3x2 - easier intensity day
W2D1: 340x5x5 - easier but still plenty of work volume day
W2D2: 295x5x2 - harder but still easy light day
W2D2: 455x2x2-3 - new PR doubles
To come back to your original question: The TM "as written" with its 5x5 @ 85-90% of 5RM on Monday in squat and press, and then a new 5RM deadlift, and then a new 1-5RM every Friday, can really run you into the ground. But if successful, it produces a weekly PR, which is a pretty big deal.
But it gets messy because you can use the basic ideas of the TM I wrote about above, to also design less brutal, less aggressive, slower progressing programming, and it's just a slightly different way of doing so than HLM, because it kind of becomes more like a general template that would be "MLH" than a specific prescription to "do this each week."