There are three basic, main types of gyroscopes. One is the rotating kind. Another is the vibrating structure type and the third is the optical variety. They each are different yet serve the purpose of helping in navigating but work in different, yet similar ways in order to serve their cause. There are also subtypes.
For instance, ring laser and fiber optic types of gyroscopes basically operate on the pricipal of the Sagnac effect which involves a beam of light being split into two parts which are sent in opposite paths and then a interface between them is created, almost magically. The pattern in thiscan tell much for direction and is an idicator of navigation.
Dynamically turned gyroscopes are yet another subtype. The rotation and the speed of rotation is the indicator which helps in navigation in this variety. Through the years, the gyroscope has evolved and as more is studied and learned about it, the more varieties can be added to the three main types.