Resolution is only one part of the picture
HD, 1080p and 4K describe different image sizes. They do not tell you how a particular stream handles motion, shadows or compression. Check the selected service’s quality options for the title and edition, especially when comparing a new release with an older restoration.
For a bigger screen
A compatible television, application and account plan may be needed for the highest available quality. A high-resolution poster on a title page is not evidence of a 4K video option. Confirm the actual playback listing before changing your television settings.
When motion keeps stopping
Try the player’s automatic quality setting, pause other heavy network activity and test whether the same problem affects another title on that service. A slightly lower stable resolution can be more comfortable than repeated interruptions at a higher setting.