Tolerance
Tolerance turns up in 2 fields: machine shop, metrology. Here is what it means to the people in each one.
Tolerance in machine shop
The total amount a dimension is allowed to vary from nominal and still be a good part.
The permitted range of a dimension, given as a plus and minus around nominal (bilateral), in one direction only (unilateral), or as upper and lower limits. Dimensions without a callout fall back on the title block, for example plus or minus 0.010 in for two-place decimals and 0.005 in for three-place. Every halving of tolerance pushes up cost, so experienced machinists ask which features really need it.
"Tolerance on that slot is plus or minus five thou, don't waste time chasing tenths, rough it and finish it once."
Tolerance in metrology
The allowed deviation from nominal that an item or instrument may show and still be accepted.
The permitted range for a characteristic, given as limits around a nominal value, such as ±0.5 % of reading for a pressure gauge or 25.000 ± 0.005 mm for a bore. In calibration the tolerance usually comes from the manufacturer's spec, a customer requirement or a regulation, and it is what as-found and as-left data are judged against. Tolerance is set by need while uncertainty is set by the measurement, and the ratio between them decides how confidently a call can be made.
"Tolerance on this transmitter is 0.25 percent of span and our uncertainty there is 0.05, so we've got 5 to 1."