Subject: Do a train's wheels travel at different speeds?

As a normal passenger train is traveling on a curved track, are the wheels 
traveling at different speeds?
What I figure is that as each car is rigid for the car to turn, the wheels on 
the differnt tracks must be spinning at different speeds so that the car will 
turn. 
That got me thinking that one track is longer than the other. As the train as a 
whole gets from station A to station B in a certain time and seemingly the 
train is moving at different speeds on each track, for the train car to remain 
intact the track that the car is moving faster on must be longer.

I confirmed to myself that logic by realizing that the tracks are parrelel when 
the train turns in a certain direction the inner track will be shorter than the 
outter one to remain parallel, and therefore again the wheels of the outer 
track must be moving quicker

Sofirst of all, is any of that right? and now, considering a train has many 
curves in different directions, would there be a significant differnce is the 
lengths of the parralel tracks. Also, if you sit on the left or right side of a 
train will you have traveled a greater distance at the end of your trip?

Re: Do a train's wheels travel at different speeds?