I don't think that this is exactly what you're asking for, but you can explore most "standard" projections below (definitely try out the first link described below):
- Take a look at [0], click "Earth" in the lower left corner, then try other projections (they appear as the "A", "CE", "E", etc. list). Drag the map around to set the projection's "center". The real time projection calculations are pretty amazing..!
- Go to [1] and toggle all of the categories ("Wall Maps", "Maps of Hemispheres", etc.) by clicking them. The maps are not dynamic / cannot be dragged around (like [0]), but this is a more complete reference list (similar to Wikipedia's list of map projections [2]). The rest of the site is also absolutely incredible (I recommend taking ~1 hour to go through the whole list of projects one by one).
[0] https://earth.nullschool.net/
[1] http://www.radicalcartography.net/index.html?projectionref