differential trace impedance for USB (90 Ohms) on 2-layer FR4 board
The reason the values differ so much is because different tools use different formulas to calculate impedance. Some are approximated closer than others, but finding exact impedance is extremely difficult if not impossible. The best tool I've used, and I still use today, is the EEWeb calculator (which you linked to in your post). That one seemed to have the best, most accurate results in my experience. There are also plenty of clones that use the same math as the EEWeb calculator so they will also be just as accurate.
Generally, when designing with controlled impedance as long as you get within +/-20% you will not notice much in the way of reflections and distortion, though of course this depends on frequency and switching speed. However, I try to shoot for about 10% over the target impedance. It's better for the Zd to be higher than the target than for it to be lower. 10% is pretty standard for most designs. In your case I'd shoot for a Zd around 100 ohms (basically 10% higher than your initial target).
The differential impedance depends on many factors including both trace width and trace spacing. For this reason it is possible to have multiple solutions trading off width and spacing. example from eeweb:
thickness=1oz, height=1.6mm, er=4
0.2mm width and 0.02mm spacing = 90.8 ohms differential
1mm width and 0.12mm spacing = 90.4 ohms differential
4mm width and 3mm spacing = 90.4 ohms differential
Choosing the best combination is dependent on several factors including manufacturability (0.02mm spacing is not typically manufacturable on PCBs), current draw(0.2mm is fine for usb but not for high current PoC) and board dimensions.
As for Ale..chenski comment, it is fully possible to make a USB device using a 2 layer 1.6mm fr4 board. It is important that you have an uninterrupted ground plane below the USB traces. This guarantees a consistent impedance and a high frequency return path. With USB 2.0 you can get away with some breaks in the ground plane with stitching capacitors though this should be avoided. USB 3.0+ would be much more susceptible to non-continuous impedance.
Marten's answer would be incorrect as seen here and here. Differential impedance is twice the odd mode impedance. Odd impedance is is the impedance of a single trace when driven in differential mode. The USB standard requires 90 Ohm differential impedance as seen here, that is across both USB_P and USB_N and would equal an odd impedance of 45 Ohm.
Sorry for the edits, can't seem to vote or comment on other answers as a new user...