Bladder stones and kidney stones are different...Bladder stones are much more common than kidney stones, so it's likely that the dog probably has bladder stones. Bladder stones are what will cause a dog to strain during urination, etc.
Also, it's important to remember about ammonium urate stones. These are seen in dogs with liver disease/liver shunt/MVD or in dalmations.
Some types of stones do not show up on x-rays which is why ultrasounds are recommended.
http://www.lbah.com/canine/urolithiasis.htm