What are the differences between all the propertys for algebra 1

There's a bunch of them!

Commutative property of multiplication and addition means a*b = b*a and a+b = b+a

associative property means a+b+c = a+c+b = c+a+b etc. and a*b*c = a*c*b etc

distributive property of multiplication over addition means a (b+c) = a*b+a*c or an+ac

there are others