Are triangulation and trilateration different words for the exact same procedure, or is there a small technical difference between the two?
If there is a small difference, which is the correct term for locating Point $P$ when the distances between $P$ and points $A$, $B$, and $C$ are known?
Finally, what is the term for the 3-dimensional equivalent with 4 spheres that GPS uses to also calculate a location's altitude?
An answer with visual examples is appreciated.
While I wouldn't say this is the mathematical definition for it, this GIS (Geographic Information Systems) post has the difference as: Triangulation is finding a point based off of given angles from other points, while Trilateration is finding a point based off of distance.
Here's an image I made based off of one of the images in that post:
So I would feel that trilateration is the better term for your context. If you want to move it up to higher dimensions, I would suggest possibly just using trilateration or 4-Point trilateration.