Boxing refers to a conversion of a non-nullable-value type into a reference type or the conversion of a value type to some interface that it implements (say int to IComparable<int>). Further, the conversion of an underlying value type to a nullable type is also a boxing conversion. (Caveat: Most discussions of this subject will ignore the latter two types of conversions.)
For example,
int i = 5;
object o = i;
converts i to an instance of type object.
Unboxing refers to an explicit conversion from an instance of object or ValueType to a non-nullable-value type, the conversion of an interface type to a non-nullable-value type (e.g., IComparable<int> to int). Further, the conversion of a nullable type to the underlying type is also an unboxing conversion. (Caveat: Most discussion of this subject will ignore the latter two types of conversions.)
For example,
object o = (int)5;
int i = (int)o;
converts the integer boxed in o to an instance of type int.
A type cast is an explicit conversion of an expression to a given type. Thus
(type) expression
explicitly converts expression to an object of type type.