There are several types of HSI systems available for light planes. One of the more common is the Bendix/King which comes standard in most high end singles and twins. The King is an electric HSI, which is nice if you have a vacuum failure. They are also slaved, so somewhere in the aircraft there will be a flux valve. They are often mounted in the wingtips, but some older aircraft can have them mounted anywhere the shop found it convenient to mount them. The actual gyro for this system is usually mounted in the tail. If you remove the back of the luggage compartment, you can usually find where this is mounted.
The other common type of HSI is the Century NSD. There are several models. Some are electric (these can be slaved), some are vacuum powered (these can also be slaved). The Century HSI usually contains it's own gyro, just like the DG you are used to.
The Sandel is also becoming popular, and to my knowledge does not contain a gyro, since it is a rear projection screen and there is no room.
So the answer to your question is it depends. Some contain a gyro, some have remote mount gyros. Some are electric and some are powered by vacuum. Some are slaved and some are not. Depends on how big your wallet is.
You can check the Bendix/King website, along with
www.centuryflight.com for Century Products. Sandel also has a website, although I have never looked at it.