smart_ptr are reference counted. While this allows for deterministic release of their resources when they are no longer referenced by any code, they do have their problems of their own: assigning references always requires the counter to be updated, circular references fail to be released automatically causing memory leaks, the memory manager is invoked more often.
The GC in .NET is a sweeping collector. It starts at any time when it feels that memory should be released (usually triggered by some memory usage condition, but not deterministic) and starts by building a list of all live references in the system (including the ones in CPU registers, nested references etc.). This works since we are in a managed environment where you cannot do pointer arithmetic etc. - the system can track all references. After the list of live references has been built, it basically releases all memory not known to be used anymore. Of course, this is just the basic sketch, for efficiency and management of unmanaged resources there is more to it like object generations, finalizers, etc., but that is not important for the basic understanding of how it works.
The IDisposable interface is used to implement the disposable pattern, which helps when you are working with objects that should be disposed in a deterministic way. The pattern is so that Dispose() is called explicitly when the object is no longer needed, therefore releasing unmanaged resources or closing handles etc., but not releasing its memory. This will be done by the GC later on, but it does not matter that this happens later, because the deterministic release of resources has already been performed.