Using the same identifier for a Type and a Class: What is the semantic effect of that syntax?

"In the file Order.cs I found an unusual construct"

There's absolutely nothing unusual about that construct.

"Notice how the identifier Customer is used with 2 different purposes. IIRC, neither C++ nor Java allows such confusing usage."

I don't know about Java but C++ certainly allow something like that:

class foo {
};

class bar {
    foo foo;
};

"Does that incantation have a special meaning and consequences?"

None at all.

"ps: I am not even sure whether my subject line is correct - Feel free to correct me."

Type and class are pretty much the same thing. You probably want to say "type and a property" or "class and a property".