Dynamic and var represent two completely different ideas.
var
Var essentially asks the compiler to figure out the type of the variable based on the expression on the right hand side of the assignment statement. The variable is then treated exactly as if it were explicitly declared as the type of the expression. For example the following two statements are equivalent
var a = "foo";
string a = "foo";
The key to take away here is that "var" is 100% type safe and is a compile time operation
dynamic
Dynamic is in many ways the exact opposite of var. Using dynamic is essentially eliminating all type safety for thet particular variable. It many ways it has no type. When you call a method or field on the variable, the determination on how to invoke that field occurs at runtime. For example
dynamic d = SomeOperation();
d.Foo(); // Will this fail or not? Won't know until you run the program
The key to take away here is that "dynamic" is not type safe and is a runtime operation