Sony pays a studio to not relase on Xbox. Xbox buys a studio to not relase on playstation. Same means, different ends.
Not exactly the same.
Historically Sony offered deals in royalties, fund development, technical support, even money sometimes etc to get some exclusive games.
Usually this was done when game runs were limited by their phisical print and didn't survive long after release date.
And usually were temporary things. Many PlayStation exclusives ended up in another system years later. Resident Evil 1 ended up in the Sega Saturn, RE2 in Nintendo 64, there were PC ports of FFVII and VIII, MGS 2 in the Xbox, GTA3 and San Andreas on Xbox, Legacy of Kain and Soul Reaver on Dreamcast. Hell, Sony even ported some games as Wipeout and Krazy Ivan to the Saturn and N64. FF XI on X360, etc. It gained mindshare for being first and in PS, but many games eventually made it to other platforms.
Now things are different, it's nearly impossible to get a TP exclusivity deal because all want to have their games uploaded in any store that grants some long term sales. Through the usual means as funding development Sony has managed many console exclusives, but temporal... KENA, Death loop, Ghost wire Tokyo, FIST, SIFU, FFXVI, Silent Hill 2, etc. But eventually the terms of these agreements end and games are released everywhere.
Buying whole publishers with MS matrix money from outside video games is something in a totally different level. Luckily Karma is a bitch and their moves and spending and good sales of PS5 have forced their hand.