Think large area/ long distance vs small area/short distance then add latitude to the equation.
If your data are already projected then you can use it or convert back to geographic coordinates.
Some points to consider from a variety of links such as ...
Geodesic versus planar distance—ArcGIS Pro | Documentation
- Although some map projections preserve some characteristics accurately, none preserve all distances correctly.
- The difference between planar and geodesic calculations of distance and direction varies with map projection and size of the study area.
- areas are defined by edges/line segments forming the border, hence area will depend on the accurate determination of distance between them
- etc
A good example of showing this is to use 4 points of long/lat to define a "square" at some latitude of some size ( keep it less than 3 degrees in E/W and N/S extent for now).
Project those points to something like UTM.
Calculate the distance between points and the area for both, using geodesic calculations for both options and planar for the projected set.
The distances along the meridians won't be too bad, but along the parallels they will differ. Now a bunch of points will form distance errors that can vary with location, hence areas bounded by the segments will result in values differing from geodesic calculations.
Tissot's indicatrix - Wikipedia
Tissot's indicatrix helps illustrate map projection distortion (esri.com)
sums it up pretty well so geodesic calculations will be better than planar but planar can be pretty good if the projection chosen is an area preserving projection. Most projections used by government maps are "compromise" meaning they are not perfect at anything but as good as they can be for the area they cover and their intent.
I am sure you know all this, but don't get hung up on how "accurate" calculations are since the measurement of location is inherently influenced by precision/accuracy issues.
Lastly location is based on a proper model of earth whose "shape" has "changed" over time as technology has advanced (eg. NAD27 vs NAD83 issues of many decades ago)...
let's leave 3D area vs 2D area out of the question for now ...
... sort of retired...