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Food
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Squirrels hoard food, finding nuts and other forms of nutrition and hiding them to come back to later. Possums, on the other hand, are scavengers. Rather than store food, they simply look for food left out by humans or other animals and eat as much as they can.
Intelligence
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Squirrels tend to be much smarter than possums. Possums essentially live in the moment; they are constantly looking for new sources of food and do not therefore need much memory or forward planning. Squirrels show forward thinking when they store food and memory when they go retrieve it again, which is a sign of much higher intellect than that of possums.
Reproduction
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Possums are marsupials like kangaroos. Marsupials are characterized by pouches; a large portion of a newborn's development is spent living inside its mother. The birthing process is therefore much more drawn out. A baby possum will slowly leave its mother's body for longer and longer time periods, whereas a baby squirrel (like a horse or a human) will be permanently out in the world the minute it is born.
Tails
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Both squirrels and possums have tails, but a possum's tail is prehensile, meaning it can grab things, manipulate things and basically function as a fifth limb. A squirrel's tail is bushy and is used to control its path when it is jumping and its descent when it is falling.
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Differences Between Squirrels & Possums
Squirrels and possums are wild mammals with many similar superficial characteristics, such as fur. Both live in trees and have tails. However, many differences separate them. Indeed, it is not very difficult to tell a squirrel from a possum because there are so many more differences than similarities. These differences are both visible to the naked eye and visible from a distance.