Isometrics are performed in a static position. They can be done sometimes with no external resistance, with a fixed object you are pushing into (overcoming isometric), or resisting a force while maintaining a fixed position (yielding isometrics).
Example, doing a bench press where you are pushing up into pins as hard as you can is an overcoming isometric. Pausing in the middle of your bench press would be a yielding isometric.
Most of the isometrics you see involving EMG research is overcoming isometrics. This allows comparison of maximum voluntary efforts to each other, which decreases the probability that variation in loading would be a factor.
However, when looking at this from a training perspective where we are using mostly large range of motion exercises and not isometrics, we lose the context of the ranges of motion the are not measured. The recruitment pattern of an exercise may not be accurately reflected y an isometric at a static point.
In some studies they try to overcome this by performing isometrics at various portions of the range of motion. This is more context, but still far from the same. When performing exercises in training, we are moving the loads through space, which changes the physics of what’s going on. This influences the resistance and stability. An isometric performed in a recovered state does not reflect how fatigue impacts the exercises over the course of a set, or even a rep.
I saved perhaps the most important for last.
When performing an isometric, you no longer have to move the joint in a specific motion. This means the muscle recruitment can drastically differ from when you are doing an exercise with motion. When contracting into a fixed object you can be applying forces that would otherwise change the motion.
So the recruitment pattern of a bench press pushing into pins would be different than doing an actual bench press. Or pulling up on something that couldn’t move would be different than doing a dumbbell shrug. The more constrained the movement is, the more you can recruit muscles different from what would be normally used in the actual motion.
So why doesn’t every study just use the actual exercise?
It’s hard to standardize loading. Meaning that, if you are comparing two exercises, how do we make sure the exercises are being compared with the exact same relative resistance and effort? If you compare two exercises but one was loaded more, it may incorrectly influence the results.
Using isometrics is one way of trying to make the loading more similar, but it’s not perfect. It still requires the participant to apply the same effort in each measurement. Which I can tell you, after doing a ton of these experiments, is unrealistic but acceptable in some conditions.