Load cell and strain gage mean the same thing.
Basically a balance bridge circuit and an amplifier.
There are a few different ways to organize the spring and the strain gage, but these are all considered load cells and different from force restoration types.
My end user (limited) understanding is very low cost devices usually employ a single strain gauge while basic-level 'load cells' usually consist of a metal anvil with two or four strain gauges affixed to measure opposite forces, allowing appropriate electronics to measure the difference, thereby providing a 'better' (more precise or accurate?) measurement.
I do know that opening my FA Intellidropper to attach a ground wire revealed what appears to be an anvil - with a single strain gauge. In use, I've found the Intellidropper to be consistent & sufficiently accurate for my needs, especially after replacing the cheesy wall wart with a power supply originally supplied with a 1st gen LCD computer display (way more robust & with the same 12V output and a higher load rating than the wall wart).
I'm a layman. Please help me understand.