what is the difference between field and a variable?

A field is a class (or struct) level variable i.e. it is visible throughout the class or struct.

This contrasts with a local variable which is only visible within the block in which it is defined. This block may either be an entire method or property or only part of it such as a loop statement.

For example:

class MyClass
{
    public int MyInt; // this is a field or class level variable

    public void MyMethod()
    {
         int i = 3; // this is a local variable
         Console.WriteLine(i);
    }
}