Yes they do, but they're far from the same thing.

Colour 35mm film - that the majority of movies have been shot on since in the 1950s - has resolvable spatial detail far in excess of even digital high definition (some say even in excess of Full Ultra High Definition).

Properly lit, shot, handled, edited and transfered, a lot of that detail would end up on the screen in cinema because they used 35mm projection. It's only TV that had the resolution problem.
Well, right up until the digital cinema switch-over began a few years ago, of course. Which was premature because now we've got cinemas which can only display 2 million pixels and tablets which can display 4 million - wtf!?

That's not even considering movies shot on larger film formats like Todd-AO and Super Panavision 70. I've got the Blu-ray releases of Baraka, Samsara and Lawrence of Arabia and let me tell you: they look incredible. Lawrence of Arabia was originally released 52 years ago.

But the state of console gaming 10 years ago was 640x480 and that was it. There was no such thing as more detail. Sure you could render higher resolutions on PC, but you always could, and you still can. And things get even messier when you consider when the PC versions of Halo: CE and 2 were released (and Halo 3/4 never were).

In other words, the instant button switch between 'classic' and 'remastered' graphics is actually underselling the difference between Xbox and Xbox One by rendering the old models and textures in modern resolutions (1600x900 atm).

To highlight the difference properly, they should stick to the resolution that the original Halo 2 on Xbox used for 'classic graphics' mode. But then everyone would want to use the new graphics for the higher resolution and complain how 'blurry' the classic graphics looked (even though that's exactly what they played in 2004 and thought it was the bomb).

At that point, might as well just get rid of the gimmicky graphics switch (and the extra memory/render burden), make the new graphics prettier and in full 1080p and have a main-menu switch to classic graphics instead (which can also be 1080p).

Understand now? I'm actually genius, ya know (joke)