In theory, your tire size of 195/60/R15 is broke down like this:
- 195 - Tread width in millimeters
- 60 - Sidewall height as a percentage of tread width
- R - Radial tire
- 15 - Rim width in inches
I say, in theory, because each tire manufacturer doesn't measure their tires the same as the next. This mainly has to do with tread width and tire height. The true measure of a tire is the rotations per mile (RPM). If you get two tires with the same RPM, they will run down the road the same (for the most part) and not mess with your speedo/odometer.
That being said, If you have a tire which is too tall, it will affect your car by showing a slow speedometer, will (theoretically) give you a higher top speed, will require more torque to get your vehicle moving, and if driving in the city will cause you worse gas mileage (due to requiring more torque).
If your tire is too short, it will affect your car by showing a fast speedometer, will give you a lower top speed, will require less torque to get your vehicle moving, and will cause you worse gas mileage at highway speeds (due to having to run the engine at a higher speed to maintain the same speed).
As @Calyth stated in their comment, the difference between the two tire sizes is not a heck of a lot, but it may show a slight difference, depending on the actual RPM for each tire.