Take a look at House of the Dragon for instance.
HD videos have a minimum resolution of 1280x720 pixels, commonly known as 720p, but can also have a resolution of 1920x1080 pixels, also known as 1080p. This increased pixel count results in clearer and more detailed images and videos.
Chameleon
1080p is considered FHD, 720p is considered HD. Yes. But you are not considering aspect ratio, which can bring about letter boxing or pillar bars.
720p videos
with an aspect ratio of 16x9 or 1.78:1 are 1280x720p. 1080p videos with an aspect ratio of 16x9 or 1.78:1 are 1920x1080. When you have a 720p or 1080p video file, where the image is 16x9 or they have added black bars to fill it out to 16x9, yes you'll see 1280x720 for 720p and 1920x1080 for 1080p.
Because aspect ratios vary by content, you could see the following for 720p:
1280 x 692 which is 1.85:1
1280 x 544 which is 2.35:1
1280 x 524 which is 2.4:1
960 x 720 is 4x3 or 1.33:1 (think old school TV shows)
For 1080p you'll see....
1920 x 1038 (sometimes 1040) is 1.81:1
1920 x 816 is 2.35:1
1920 x 800 is 2.4:1
1440 x 1080 is 4x3 or 1.33:1 (think old school TV shows)
Of course for 720p or 1080p having an aspect ratio that isn't 16x9 means you'll have black bars top and bottom, or on the left and right, when watching on current wide screen TV's, unless the TV's "zoom" features are used to stretch the picture to fit the screen.
For example, when I watch this particular episode of House of the Dragon on my Sony 43" 4K TV, using my FireTV stick and the Max app, I do have slim black bars above and below the picture. Its not a 16x9 image.
Your MediaInfo shot is even telling you its a 2.0:1 aspect ratio as Max hasn't included the black bars in the image to pad it out to 1280x720.
1280 x 640 is 720p at 2.0:1 aspect ratio (no black bars included to make it 16x9). It is not 640p.As further example, watch The Dark Night Rises on Max. its shot at 2.4:1 so I'm sure you'll see black bars top and bottom. Then download it using StreamFab. It should download at 4K since its older. While 4K is 3840x2160 when 16x9 or 1.78:1 aspect, The Dark Night 4K downloads at 3840x1600 because its 4K at 2.4:1 aspect.