Please explain with theoretical concepts and a brief example.
Tolerance is a property of a design. Tolerance is a acceptable deviation from plan that is designed as part of your acceptance criteria. You document this in your drawing/contract either as a general tolerance or specific demand for one feature in your part. If a part meets your tolerance then you have agreed to accept it as is if not then the part is rejected.
Rejection usually leads to making a new part, fixing it or in some situations you have quality classes and use lower quality products for less demanding jobs. Later is typical in semiconductor industry and lcd panel manufacturing. Specifying tighter tolerances means that it takes more effort to produce the components leading to higher cost. On the otherhand you pay more for parts but you may gain this back in turn by having less problems in assembly and use.
Measurement uncertanty is a property of physics, and measurement. Things change all the time and on the lowest level this is bounded by Heisenberg uncertainty principle, but you need not go this deep to notice it.
Take a simple experiment of measuring the length of a pen. No matter how many times you try you always get slightly different results because of how your experiment is set up. There are ways to make your experiment better, but as you increase accuracy your setup becomes more combersome to conduct. Imagine how much a 1 degree temperature difference affects the length of your pen, or how much the movement of your house due to traffic affects it.
Measurement uncertainty is just a intervall that tells how reliable your measurement result is. Its not part of your design but part of your measurement apparatus.
Measurement uncertainty is not linked to tolerance although the need for tolerance is caused by much the same reasons as measurement uncertainty. Tolerance is usually quite much higher than measurement uncertainty, even if some tolerances are very hard to measure.
As a side note if you put very stringent tolerances on your design then you also need to verify those. So you need better equipment and better planned experiments to verify this. And if you do not then what is the purpose of having such a high tolerance?