This issue deals with an important point when it comes to GIS data: Spatial Resolution & Precision.
You have said in the comment that that a point (0, 45) & (0, 46) might appear to be on the same location given a low enough zoom level. How do you tackle this? Do you want the tolerance value to change depending on the Zoom level? Or do you want it to be fixed? Say that two points are coincident, if they lie within 2 m of each other?
In either case, you will need the distance measurement.
For Points it doesn't make sense to use exact point coincidence or intersection, since that is pretty much useless due to floating point precession used in computer systems.On a related note, Every Computer Scientist Should Know About Floating-Point Arithmetic