Science categories break things down into their basic components. Examples: things that return to their original position when you let them go vs. things that don’t; 1st, 2nd & 3rd-class levers .
Math categories look at numbers or geometric patterns. Examples: Number of pivots; inputs and outputs move in the same vs. opposite directions; inputs that make a full circle vs. those that don’t.
Engineering categories are about what things are used for. Examples: things that cut vs. things that squeeze vs. things that mash, etc.; things you find in the bathroom vs. things you find in the kitchen vs. things you find in school.