The problem is easily avoided once you learn a bit about resolution. Different monitors can, regardless of size, handle different resolutions.
Resolution is the number of pixels used to display the interface expressed as width times height.
The figure above shows the relative amount of space afforded by three different resolutions. Obviously you never get a big gap along the right hand side and the bottom, each resolution expands to fill the available viewing area of the monitor. The effect is that as resolution size increases the size of all controls and windows decreases when using the same physical size of monitor. This is because it has to cram in so many more pixels into the same space. The answer is yes, and you don't have to write several versions of the same program.