You're probably comparing a linear polariser with a circular polariser. The linear polariser is a basic filter that only passes light waves polarised in a particular direction. That works either way round, and you can combine two of them to produce a variable density filter - by rotating the second polariser, it passes most of the light when the polarisation directions are the same, and a minimum amount when the polarisation directions are at 90 degrees to each other.

Many older polarising filters were linear ones - and that sounds like what your rectangular filter is.

But there's also a polarising effect when light reflects off glass or water at an angle (how much varies with angle). - that's why rotating a polariser can often reduce reflections from water or glass.

Unfortunately, that can cause problems when it happens in the metering/AF systems of a camera. So the manufacturers came up with the idea of circular polarisers - these are more expensive than plain linear polarisers, and combine a linear polariser (at the front) with a second layer that converts the linearly polarised light into circular polarised light - which doesn't suffer from the reflection effect. But that means they only work like linear polarisers one way round. (For details of how the second layer - a quarter wave plate - works, see https://en.wikipedia.org/wiki/Waveplate).

The colour shift effect is probably similar to that used in geological microscopes, where it can be used to help identify materials in thinly sliced rock samples.