Eyes generally move in a piecewise linear fashion, but they are attracted by "interest". Certain things along the way may distract they eye. I HOPE SO, otherwise how could we drive a car? This also makes speed other than constant. Moving your focus from one side of the screen to the other goes quickly enough, but interest and comprehension lag a little behind - again, according to various interests.
Also, we do not necessarily encounter or process all the information along the way. This was once very important to me in a dark grocery store parking lot. Walking out of the store, I quickly scanned the parking lot for anything that would make me uncomfortable. A young man and his girlfriend were walking away from me. The young man apparently saw my eyes scan the parking lot. Of course, somewhere in that scan was his girlfriend. The young man was very angry with me for "looking at" his girlfriend. Truthfully, she was in the scan, but "looking at" her was not. I was falsely accused. Tricky things, eyes.