The confusion cleared up
"GPS" refers to the technology — the Global Positioning System — that your device uses to determine your position via satellites. "MGRS" is the coordinate format: the way that position is expressed. You can use GPS technology and display the position in MGRS format.
WGS84 decimal degrees
Most consumer apps — Google Maps, Apple Maps, Waze — use WGS84 decimal degrees: 52.3676, 4.9041. This is accurate, but has drawbacks in the field: the numbers are long, not intuitive, and difficult to communicate.
DMS (degrees, minutes, seconds)
An intermediate format: 52° 22' 3.36" N, 4° 54' 14.76" E. Slightly more familiar to sailors and aviators, but still cumbersome for land operations.
MGRS: designed for the field
MGRS was specifically designed for military and field operations. Advantages: codes are shorter (31U ET 12345 67890), the grid is rectangular (easier to calculate), precision is adjustable (4-, 6-, 8-, or 10-digit), and the code is less prone to reading errors over radio.
When do you use which?
Use WGS84/decimal for: navigation apps, online maps, aviation, interfacing with external systems.
Use MGRS for: military operations, SAR, mountaineering, expeditions, communication between teams, operational documentation.
MilMap supports both
In MilMap you can set which coordinate format is used per map. You can always switch without losing data — all conversions are accurate and automatic.