Does the screen resolution matter for video players? Following on from my question over at video.ex, do media/video players downscale a video if the resolution is bigger than the screen resolution?

I'm wondering if it really matters if a phone/tablet says it supports HD or Full HD if the screen resolution is lower than HD.

It might depend on the Android OS version but what resolutions does the default player support? Do different apps support different resolutions?
Yes, most video players will automatically up- or down-scale videos to fit the screen. Android OS itself, and video player apps, don't have a limit on video size. Obviously each device's hardware is only fast enough to decode so many pixels per second, so there's an upper limit on video resolution, data rate, and frame rate for smooth playback.

Like any other playback device, if an Android device doesn't have enough pixels on its screen to play 1080p video, it can't be advertised with the "Full HD" trademark logo.