Why do some people pay less to get into the museums?

It depends on your passport.
Many museums and concerts have two prices, the local Russian price and the foreigner price. The government tries to make things affordable for local residents but also charge a fair price for foreigners.
There is passport control at big museums like the Hermitage and it is very difficult to get lucky to be allowed to pay a lower price.
Usually the price is clearly market in English for the tourist price and in Russian for the local price. Fortunately, even the foreign price is a good value.
Here is a great tip: The Hermitage Museum has free entrance on teh first Thursday of every month!
David and Maria, www.sennaya.com