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If you’re talking about strips that look like this:
I believe that most brands use Benedict’s reagent: copper sulphate, sodium citrate, sodium carbonate. It interacts with reducing sugars (like glucose) and the colour goes from blue to light green to green to brown-green to brown-red, depending on concentration.
Those are used with urine, not blood. Urine is yellow-ish, but since it’s just a drop, it doesn’t stain the strip; instead, the blue tip changes colour as it reacts with the glucose in the urine. Then you compare that coloured tip with a chart, and you get an idea of the concentration of glucose in your body. Picture related:
I remember seeing those bottles in my bathroom all the time as a kid (my sister is diabetic).
It is roughly the same idea as the one behind the litmus test for pH, indeed. The difference is which substance you’re putting there (Benedict’s reagent vs. pH indicators) and which substance you’re testing for (glucose vs. H₃O⁺ / OH⁻).