PowerBASIC for Windows
PowerBASIC for Windows is an implementation of PowerBASIC. Other implementations of PowerBASIC.
PowerBASIC for Windows (a.k.a. PB/Win) is the Windows compiler for PowerBASIC. This is the version that is meant to deal with windows, and there is an add-on (called PowerBASIC Forms) that can make this task easier.
It's important to note that there are some fairly major language differences between the DOS and Windows versions of PowerBASIC.
PB/Win was originally named PowerBASIC DLL Compiler (PB/DLL), which reflected its original purpose: writing DLLs for Windows, both 16-bit and 32-bit. (Normal applications were supported in a manner similar to other contemporary languages, using resource scripts to draw windows.) With version 7 the name was changed to PB/Win and 16-bit support was dropped.