Screen wash is the designed to remove ink before you reclaim your screens. There are different types of screen wash. Some brands of screen wash are for removing different inks- such as plastisol or watebase ink. Also, some screen wash brands will degrade emulsion, while other screen wash options will remove the just ink and leave the emulsion intact so you can catalog the screen for later printing.
so only use screen wash if you are done printing and want to reclaim your screen printing frame. Press wash is used on press to change ink colors without degrading the emulsion/ stencil. For example- you may print 24 black shirts with white ink- and you have 24 more white shirts you want to print with black ink; press wash will allow you to remove ink in the screen and add a different color with out harming your emulsion the way screen wash may break your emulsion down.