So, leaving the US at an airport, you go through security. Different airports have different "fastpass" options-CLEAR, TSA pre check, and sometimes for Business/First. When you arrive in an international country, you'll go through immigration (their's). If you are business/first you might get a "fastpass" there (usually prior to disembarking the plane the flight attendant will hand you a piece of paper which says something like priority). Having waited in line at NRT for two hours at immigration-this will be worth it.
Once you leave for the US, again, security may or might not have a "fastpass" for screening/security if you're business/first/elite. Then, upon arrival in the US is when the Global precheck is helpful. There are usually 3 lanes at immigration (big picture, I know those with visas fall in somewhere) : US passport holders/non US passport holders/Global Entry. The GE line is the shortest, and there are kiosks where you scan your passport, your fingerprints, answer some questions, a truly horrible photo is taken and a slip of paper shoots out that you take to the immigration official. It definitely speeds the process...to the point that we don't wait in line for immigration but half the plane catches up for us as we're reclaiming luggage

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TL;DR TSA precheck gets you through US screening more quickly, Global Entry through immigration Stateside more quickly. Biz/first may or may not have additional front of the line privileges depending on the airport.