It is because most of the films on that channel, if not all were shot before they changed the aspect ratio to what it is today. As a result the films fill the screen in SD, but not HD.
Aspect ratio has nothing to do with standard and/or high definition.
Up until the 90ies, most film was shot on 35mm film. If the original reels are still available, these can be used to make a high-definition version of any film.
Take this movie as an example:
A Bridge Too Far, 1977 - has been digitally remastered and can be seen in its entirety on Youtube. You can select up to 1080p quality.
The aspect ratio.... is different than 16:9, I grant you that. It is 1.37:1 instead, resulting in a wider screen, which in turn on a 16:9 screen would result in black bars at the bottom and top. For television broadcast, sometimes movies are cropped so they fit on the screen.
As far as TCMHD goes, they have many digital tapes with movies that aren't necessarily in HD, but are of better quality than SD broadcast on 480i. These tapes were often made in the 90ies, before actual High Definition was even an issue, on DVCPRO or BETACAM tapes. These tapes contain a version of the movie that was also derived from the original 35mm film, edited for broadcast, and is still in use today. The quality of the movie on the tape is significantly better than SD, and when these tapes are used to broadcast movies - and many stations that broadcast pre-90ies movies probably use these kind of tapes from their library - via a HD medium, you will see a significant improvement of quality.
In the industry, to be considered "high definition", it has to have a better resolution than 480i. It doesn't have to be wide screen or conform to any sort of aspect ratio. As a matter of fact, in the late 90ies and early 2000s, quite a few TV's were sold - especially the rear-projection kind - that could accept and show 720p HD through component cables, but had a 4:3 screen resolution. Most people just used them as SD TV's. Often, these could also use 4:3 resolutions like 800x600 and 1024x768 to display video, and purely from a technical/theoretical standpoint, those resolutions ARE "high definition", they just aren't one of the currently defined 720/1080 standards.
In any case: TCM HD looks pretty darn good!