There seem to be many misconceptions about the difference between polyurethane and polyethylene foam. Here are some facts to help guide you in understanding how the specifications of these foams differ, and how they relate to gymnastics products made with one (or both) of the foam types.
Is there a difference in the quality of these foams?
Quality doesn't affect the difference between these two foams. They have different properties and thus are used in different gymnastics or martial arts applications. One is not better or worse than the other; they are different.
What is the difference between polyethylene foam and polyurethane foam?

What is polyethylene foam?
Polyethylene is a strong closed-cell foam. The polymer molecules are cross-linked, providing greater rigidity, so this type of foam is often referred to as "cross-linked" or "cross-linked polyethylene" foam. The cross-linked nature of this foam type makes it work very hard to snap back to its original shape quickly, which has the effect of introducing a little "bouncing" in addition to providing shock absorption. Due to its rigidity, polyethylene does not widely distribute fall energy. You can think of it as "shockproof" foam.
This foam is traditionally used in relatively thin (1" to 2") gymnastics products, so it needs to be overall strong. It provides a combination of lightweight cushioning and fall protection while still providing a firm foothold when landing. This foam is typically used in applications where the foot or hand is on the ground and you want to avoid spraining your ankle or wrist. It is commonly found in standard folding mats, gymnastics floors (such as carpeted foam rolls), martial arts floors, and portable, slatted, cheering floors (such as flex rolls). It is also sometimes used as a top layer of softer foam to provide better foothold, with a lower layer of softer foam adding some shock absorption.
What is Polyurethane Foam?
Polyurethane is a softer open-cell foam that comes in varying degrees of durometer. Because the cells are open and uncrosslinked, air can flow through the foam like water can flow through a sponge. This property makes the foam softer and better able to absorb impact energy. It doesn't spring back as quickly as polyethylene and distributes the energy of compression more widely.
This foam is typically used in products that need to provide more impact protection, so it is thicker (4"-32" thick) and softer. It provides more cushioning when your body is on the ground rather than your feet or hands. Common products that use this foam are throwing mats, practice mats, landing and stunt mats, ramp mats, and other items used to prevent falls and injuries.
Have polyurethane and polyethylene ever been mixed in the same product?
Yes. There are some products that use both types of foam in combination. Softer polyurethane will be used for the body, bottom and core of the product, while a thinner, stronger layer of polyethylene is only added as the top surface. This combination creates a thin, firm top and a tall, soft bottom. When this combination experiences impacts such as foot landings, it provides enough stiffness to keep the ankle from rolling. However, the entire softer base layer compresses at the same time, creating a cushioning effect. This is especially useful when you normally land or stand on a mat, but want to be able to "soften the blow" when you hit the mat.
Have polyurethanes with different ILD contents been mixed in the same product?
Yes. Many thick mats (landing mats, practice mats, pit mats, crash/stunt mats) will use a combination of higher and lower ILD foam in different layers. Also, generally a higher ILD foam (harder) will make up the top layer, while a lower ILD (softer) foam will serve as the bottom layer. The top layer is not as strong as polyethylene foam, but will provide more foundation than if the entire pad were made from softer foam on the bottom.
For example, you might see that the bottom 50% of your practice mat is 36 ILD, while the top 50% is 75 ILD. Coming down from the vault, this will help keep your feet firmly on the ground, but if you land on your back or tailbone, it will cushion your fall and protect you. On the other hand, when stuntmen are thrown out of bar windows, they don't even try to land on their feet. The idea here is to cushion falls when the whole body hits the pad. So a 24" thick stunt mat might be made entirely of very soft 24 ILD foam with extra air chambers, and since it's so soft you need a lot of thickness to absorb the impact.
How do we measure polyurethane hardness?
The first thing we need to look at is hardness, not density. The two are often mistakenly thought to be the same thing, and they can be related, when in fact they are different characteristics. Density tells us how much an item weighs per unit volume, but it doesn't necessarily indicate how stiff it is. When we look at gymnastics foam, we are interested in hardness, which tells us how soft or hard the foam feels when we step on it or fall on it. Foam hardness is measured using a unit of measurement known as Indentation Load Deformation (commonly referred to as ILD). In gymnastics applications, you will typically see polyurethanes with ILD numbers between 24 and 75. The higher the number, the firmer the foam. The lower the number, the softer the foam. Therefore, 36 ILD foam is quite soft,
