Time.deltaTime not consistent over time

I am trying to do network time synchronization across clients, but I noticed some weird behavior and setup a simple project to test Time.deltaTime as it counted up. All I do is have a variable in the project that starts at 0 and holds the milliseconds since the program started. I display this on the screen and then open the program in 2 separate windows. I then compare the difference in the time displayed, and instead of the difference staying constant, it fluctuates quite substantially.

float counter = 0.0f;

void Update() {
    counter += Time.deltaTime * 1000;

Unless I am understanding this incorrectly, no matter the framerate or when the players were opened, the difference between the value for counter should remain constant. Am I approaching this incorrectly, or is this a possible bug?

Yes, accumulating deltaTime into your own variable will always be less accurate than measuring Time.time directly.

Simply use Time.time instead of your counter variable and you should get much better results.