The Saver Award destinations are quite limited. Do the standard awards allow you to fly between any two cities in the continental U.S.?
Both Standard and Saver awards allow you to fly any valid routing operated by United, United Express, United Connection, or Copa— not just in the continental U.S.
The link you provided merely suggests routes where saver awards may be available; it is not a comprehensive listing. There are no geographic limitations on any United award flight options (Standard and Saver already mentioned, plus Star Alliance and "Air Partner"), although the redemption levels will differ depending on where the travel is between. In theory, you could travel YVR-KWI on a single award for 40,000 miles, but BDL-IAD could be had for as little as 10,000.
Standard awards are somewhat analogous to full fare tickets, and saver awards to discount tickets. The redemption level for (cost) for the standard award is quite high, but if there is any seat to be had on the flight, you can get it. The redemption on a saver award is only half as much as a standard award, but they are capacity controlled, and much harder to come by on many routes. Generally, an airline will only make a saver award available if it believes, based on historical sales information, that it will not be able to sell the seat to a paying customer. Today's full flights and shrinking capacity are why saver awards are harder to come by.
One more note: the Standard and Saver award terminology is applicable only for awards redeemed exclusively within the United and Copa systems. If you add even one segment on a partner airline, it becomes a Star Alliance award or Air Partner award as the case may be, and all seats are capacity-controlled like Saver awards are. You cannot pay double the miles to secure a seat on Lufthansa or EVA or even US Airways.
Standard awards are available on the regular United and Star Alliance flights, so no - not between any two cities, only where there are United and partners' flights. Even then, the award sits are limited (although the United credit card holders are promised to be given a standard award sit on any flight that has seats for sale).