Samsung phones use both, in a very literal sense. Their flagship devices usually have both Snapdragon and Exynos variants for different regions, and their lower end devices are mostly Exynos across the board.
The S23 line was an exception in using Snapdragon worldwide, but then the S24 line switched back to using Snapdragon in NA and Exynos everywhere else, except for the S24 Ultra which is still Snapdragon everywhere.
Yes it's a confusing mess, and it's arguably misleading when the predominantly NA-based tech reviewers and influencers get the usually superior QCOM variant, and promote it to a global audience who may get a completely different SOC when they buy the "same" device.
Last time I checked, the latest Qualcomm Snapdragon was faster and more energy efficient than the latest Exynos. Especially the top-binned chips that Samsung gets.
Still, the fact that Samsung can swap out the chip in their flagship product with virtually no change other than slightly different benchmark scores means that these chips are pretty much fungible. If either manufacturer runs into serious problems, the other one is ready to eat their market share for lunch.
Yes, Exynos is still behind in performance and thermals. Exynos modems are also still garbage and plague Pixel phones with issues. Though slowly improving with each generation, it's awful that it's being troubleshot in public over years.
