Do scientific models have to exactly match reality?

strictly - no model can precisely matches reality, unless we have a perfect understanding of reality, which I'm pretty certain we don't as yet.

Scientific models are supposed to based on the best understanding of reality, that exists at the moment. Frequently taught by a history of scientific models, which runs kids through what was thought to be correct, then tells the kids why that was found to not be correct. [IMHO probably the biggest factor in putting kids of science, ie "Why are we learning this? Next year we'll be told to forget it all, as we'll be told what we learnt this year is wrong." ]

Engineering models- tend to work with "good enough for a given purpose" and what's good enough depends very much on what the model is being used for.

eg much of fluid mechanics relies on something called the continuum hypothesis. That's an assumption that's known to be false,but which simplifies the maths, and in under most conditions the resultant predictions aren't significantly different from reality. The assumption runs so that when dealing with problems such as the buoyancy of a ship, there's really no need to worry about the water being made of molecules. With that assumption in place the water is treated as being a substance that could be divided into infinitely small things that still water. It doesn't make much difference to the results. Could say similar applies to calculus and it's concept of the Infinitesimally small.

Engineers operate in the world of reality. For that reason one of their best developed skills is know how sceintic models or equations match up to reality. Also most all of the theory you see in physics and chemistry books has to be adjusted to fit the real world.

Take equations that use the acceleration of gravity as one of the functions. In school we always assume it to be a certain number but in reality it can vary due to location on the earth both horizontally and vertically.

Einstein showed that Newton's law of gravity was lacking at high velocities, nevertheless, NASA still uses Newton's mathematics when they launch satellites.

A model only applies when the correct criteria are met. A model is not applicable if the circumstances for which it was intended do not exist.