For an area, you can choose to take the centroid as coordinates. There are multiple data sources for an area with the same name. Depending of each one, the polygon representing it may vary. These differences can come from historical reasons, disagreement about the area coverage,... So, the resulting centroid may change too.
Think about sea naming and coverage. Where is the "limit" between 2 seas for example? In this particular case, the name refers both to a New York quarter and a sea area (according to Wikipedia https://en.wikipedia.org/wiki/Jamaica_Bay). The tools can't guess.
Sometimes, to describe/summarize your area, you prefer to use a point in polygon (also named point on surface) or pole of inaccessibility and it differs from centroid. See this image for difference centroid and point on surface http://www.h2gis.org/docs/dev/ST_PointOnSurface.png and this article about an approximation of pole of inaccessibility https://blog.mapbox.com/a-new-algorithm-for-finding-a-visual-center-of-a-polygon-7c77e6492fbc
Another difference can be related to coordinate rounding choices.