They are completely different.

Unit testing is concerned with verifying that small chunks (functions/methods) of code work in isolation. For example, if you have a function that adds two numbers, then your unit test must test whether or not the function calculates the sum correctly.

System testing is concerned with validating whether or not your full system meets the requirement specification. This type of testing is used to determine whether or not the system developed as a whole does exactly what it is expected from it. For example, if you were tasked to develop a calculator, then your system testing must show that all operations that are required by the user are available.

They are completely different.

Unit testing is concerned with verifying that small chunks (functions/methods) of code work in isolation. They should test cases of common usage, edge cases and any case in which an error can occur. For example, if you have a function that adds two numbers, then your unit test must test whether or not the function calculates the sum correctly.

System testing is concerned with validating whether or not your full system meets the requirement specification. This type of testing is used to determine whether or not the system developed as a whole does exactly what it is expected from it. For example, if you were tasked to develop a calculator, then your system testing must show that all operations that are required by the user are available.