Deploying links to fact-checking websites (so-called "snoping") is a common intervention that can be used by social media users to refute misleading claims. However, its real-world effect may be limited as it suffers from low visibility and distrust towards professional fact-checkers. As a remedy, Twitter launched its community-based fact-checking system Community Notes on which fact-checks are carried out by actual Twitter users and directly shown on the fact-checked tweets. Yet, an understanding of how fact-checking via Community Notes differs from snoping is absent. In this study, we analyze differences in how contributors to Community Notes and Snopers select their targets when fact-checking social media posts. For this purpose, we analyze two unique datasets from Twitter: (a) 25,912 community-created fact-checks from Twitter's Community Notes platform; and (b) 52,505 "snopes" that debunk tweets via fact-checking replies linking to professional fact-checking websites. We find that Notes contributors and Snopers focus on different targets when fact-checking social media content. For instance, Notes contributors tend to fact-check posts from larger accounts with higher social influence and are relatively less likely to endorse/emphasize the accuracy of not misleading posts. Fact-checking targets of Notes contributors and Snopers rarely overlap; however, those overlapping exhibit a high level of agreement in the fact-checking assessment. Moreover, we demonstrate that Snopers fact-check social media posts at a higher speed. Altogether, our findings imply that different fact-checking approaches -- carried out on the same social media platform -- can result in vastly different social media posts getting fact-checked. This has important implications for future research on misinformation, which should not rely on a single fact-checking approach when compiling misinformation datasets.