Datum: with an ellipsoidal earth, two parameters define the best fitting ellipsoid, but three are used:
Any two define the datum and third can be derived, but different datums select different combinations for their definition.
e -- eccentricity; e² = 2f - f² (used in most projection formulas)
Take this shape, and a starting point (now usually defined with coordinates so that Greenwich and equator are on the zero longitude and latitude line, and an orientation), and get lat-long grid
Developed in 19th century, local datums gave best fit for the geoid in area. At that time they could not do a worldwide fit, and original errors in measurement mean some of these are very different from currently accepted values.
At least a half dozen datums are in wide use, and over 100 have been defined.
With satellite positioning and gravity, true geocentric coordinates and earth shape are possible.
World wide datums: WGS84 for the world and NAD83 for North America, which replaced NAD27; shifts up to several hundred meters in lat-long coordinates if using different datums
The US will soon get 4 new datums, one for the region on each tectonic plate (Caribbean, North American, Pacific, and Phillippine). Nominally named for 2022, these are being delayed.
Other datum topics: