How do I check if a type is a subtype OR the type of an object?

Apparently, no.

Here's the options:

• Use Type.IsSubclassOf
• Use Type.IsAssignableFrom
• is and as

Type.IsSubclassOf

As you've already found out, this will not work if the two types are the same, here's a sample LINQPad program that demonstrates:

void Main()
{
    typeof(Derived).IsSubclassOf(typeof(Base)).Dump();
    typeof(Base).IsSubclassOf(typeof(Base)).Dump();
}

public class Base { }
public class Derived : Base { }

Output:

True
False

Which indicates that Derived is a subclass of Base, but that Baseis (obviously) not a subclass of itself.

Type.IsAssignableFrom

Now, this will answer your particular question, but it will also give you false positives. As Eric Lippert has pointed out in the comments, while the method will indeed return True for the two above questions, it will also return True for these, which you probably don't want:

void Main()
{
    typeof(Base).IsAssignableFrom(typeof(Derived)).Dump();
    typeof(Base).IsAssignableFrom(typeof(Base)).Dump();
    typeof(int[]).IsAssignableFrom(typeof(uint[])).Dump();
}

public class Base { }
public class Derived : Base { }

Here you get the following output:

True
True
True

The last True there would indicate, if the method only answered the question asked, that uint[] inherits from int[] or that they're the same type, which clearly is not the case.

So IsAssignableFrom is not entirely correct either.

is and as

The "problem" with is and as in the context of your question is that they will require you to operate on the objects and write one of the types directly in code, and not work with Type objects.

In other words, this won't compile:

SubClass is BaseClass
^--+---^
   |
   +-- need object reference here

nor will this:

typeof(SubClass) is typeof(BaseClass)
                    ^-------+-------^
                            |
                            +-- need type name here, not Type object

nor will this:

typeof(SubClass) is BaseClass
^------+-------^
       |
       +-- this returns a Type object, And "System.Type" does not
           inherit from BaseClass

Conclusion

While the above methods might fit your needs, the only correct answer to your question (as I see it) is that you will need an extra check:

typeof(Derived).IsSubclassOf(typeof(Base)) || typeof(Derived) == typeof(Base);

which of course makes more sense in a method:

public bool IsSameOrSubclass(Type potentialBase, Type potentialDescendant)
{
    return potentialDescendant.IsSubclassOf(potentialBase)
           || potentialDescendant == potentialBase;
}

typeof(BaseClass).IsAssignableFrom(unknownType);

You should try using Type.IsAssignableFrom instead.