Casting is when you take a variable of one type and change it to a different type. You can only do that in some cases, like so:
string str = "Hello";
object o = str;
string str2 = (string)o; // <-- This is casting
Casting does not change the variable's value - the value remains of the same type (the string "Hello").
Converting is when you take a value from one type and convert it to a different type:
double d = 5.5;
int i = (int)d; // <---- d was converted to an integer
Note that in this case, the conversion was done in the form of casting.
Parsing is taking a string and converting it to a different type by understanding its content. For instance, converting the string "123" to the number 123, or the string "Saturday, September 22nd" to a DateTime.
