WinPE is the plain WinPE boot environment.
Windows Setup is WinPE + Setup files.
WinRE (Recovery) is dynamically created on the Recovery partition from a WinRE.wim file found on the Windows C:\ filesystem. This Recovery environment copies any installed drivers so it's compatible with your system. WinRE is a derivative cousin to WinPE.
WinPE is always provided on the Windows ISO for deployment scripting. It has a separate set of optional packages (including PowerScript and .NET libraries), which are not interchangeable with normal Windows packages. There is no need to add them to Windows Setup, since Windows Setup only has one job: prepare the system, and run Setup.exe
While Macrium could use the boot.wim image, their instructions require you to download the Windows ADK (which customizes WinPE). The reason is they depend on ISO creation tools found inside the ADK toolkit. Unlike most (cough, cough) public files, ADK is licensed intellectual property of MS. Macrium as an official MS partner cannot redistribute those files themselves.
NTLite doesn't require ADK, because it uses other open-source libraries to do the same tasks.