When we are talking about Push-Out windows what we really mean is pull-in, because that is how you actually open the window. From the handle you pull the window sash in to open the window. There are some actual Push-out windows where you open the casement windows out instead of in.
If your window won't stay up when you open it you will probably need a window sash balance repair. What this entails is to buy a new window sash to replace the one currently in your window frame. You will want to make sure that the sash balance is rated to carry the weight of the sash in your window.
According to the dictionary and wikipedia, storm windows are secondary windows installed to provide additional protection from harsh weather. These windows can be installed outside or inside of the normal windows in a home. In the past these windows were in wood frames and could be taken down during warmer weather so that the windows of the home could be opened to let in air from outside.