Last time I got new tyres I was advised that as they were out of stock of the particular size I was after (195/60/R15) and since they were part used tyres, I should be OK going with a slightly smaller tyre (185/60/R15) and that this would have "no effect" on anything.
Since if it really had "no effect" on anything there would be no need for the differing tyre sizes, what are the side effects of using the wrong tires?
In theory, your tire size of 195/60/R15 is broke down like this:
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.
I have been using one size up tires on my sub-compact car for 21 years. (Nearly 300,000mi) While they do have more rolling resistance and cost $10~20 more per tire, there are some real advantages. Improvements in Ride Smoothness, Snow Traction, Highway Mileage, Cornering and Emergency Handling. Yes my Spedo/Odometer are under estimating slightly, (Just under 8%) but this too has its advantages. Lower reported mileage = better Selling/Trade-In Value. (I've Purchased 3 Cars & 2 Motorcycles, but have yet to Sell one!) Under Reported Speed is nice too If you like to Speed just a bit. (25=27, 35=38, 45=48.5, 55=59.4, 65=70, 70=75.6, 75=81) So if like most people you Speed a little but try not to go more than 5mph over, Drive the exact reported speed and you're going 2~6 miles over. And if you ever get a Ticket: Just get a Spedo Calibration Test done and bring it to Court. The Judge will reduce or through out the ticket.
Depending on the car, if you only switch on 1 axle then it could confuse the ABS system, which would detect different speeds front and back. On some vehicles with 4wd it could cause major issues with the central differential.
