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Imperial screw gauge relates to diameter by the linear rule 0.060 + 0.013 x gauge inches, so a number 8 screw is 0.164 inches or 4.17 mm - close to an M4. Lengths are quoted separately in inches, so a 8 x 1.5 inch screw is 4.17 mm by 38.1 mm in metric terms.
Gauge to diameter
inches = 0.060 + 0.013 x gauge
Metric
mm = inches x 25.4
It is the standard approximation for wood screws. Machine screw standards specify exact diameters per size, which differ slightly.
For clearance holes usually yes, but threads are not interchangeable - pitch and thread form differ between the systems.