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Is a 1.5mm hex key and a 1/16" hex key interchangeable?

Looking on a ruler, my 1.5mm key looks to be 1/16"

The reason I ask is that it looks like I have threaded saddle height screw on the D string of my Classic Stingray 4. My teacher is the only one who has made adjustments to the string heights until today when I tried to make an adjustment. I had a hard time getting purchase, I then managed to lower the string, too much, and now I can't get it back up. Looking down in there I can see that the hexagonal walls are very worn out. EBMM is sending me new screws, but was wondering if it's worth going out and getting a 1/16" key.

I have seen in other threads mention of a metric vs. standard issue.
 
no! no no no!

you'll absolutely strip stuff out if you use the wrong key, especially on small stuff under pressure like saddle height screws.
 
Two standards can (perhaps) be found in American toolboxes.

1. Metric (mm)
2. SAE (standard american equivalent)

Although some will be close-you've asked if two different standards are identical? Nope...
Most times-when I've tried a tool in the other standard, it's been a no-go.