There is no garbage collector in either language. At least, not as part of standard compliant implementations.
Note that C++ had language restrictions which made it hard to implement garbage collection. Some of those rules have been relaxed in the latest standard, C++11. So in principle it would be possible to implement a standards compliant c++ garbage collector now.
The standard approach in C++ is to use smart pointers to automatically manage memory.
There’s an interesting article here, containing some useful links. From the comments you might be able to see how difficult it is to reconcile GC with idiomatic C++.
7
solved Can we manually operate the garbage collector in C or C++? [closed]