A theoretical probability usually assumes a perfect situation, such as the tossing or spinning of a coin. Theoretically there is an equal probability that it will fall to show a head or a tail. The probability of either is exactly 1/2.
If a coin is tossed or spun 100 times the expectation theoretically is that there would be 50 heads and 50 tails. Experimentally this will probably not be the case, because of factors that are not taken into account. However, the result will probably be approximately 50:50. Tossing or spinning a coin 1000 times should yield a similar result.
There is also a small possibility that the coin will stop on its edge, neither head nor tail. This could occur a few times. The theoretical probability doesn't take this into account at all. Nor does it allow for bias caused by the irregular distribution of metal or impurities, or slight differences caused by engraving.
The way the coin is tossed or spun is another unmeasurable factor which isn't taken into account theoretically. Theory assumes a perfect or pure situation, whereas in reality this cannot be achieved.
Weather is a particular example of uncertainty, because it isn't possible or practical to take into account all factors controlling the weather. Any attempt to do so would probably affect the weather itself! So theoretical models are used, usually in computers because of the complexity. But the computers are only applying theory.
That's why experimental and theoretical probabilities differ. And there's a probability that empirical and theoretical results will be the same. What matters is the confidence assigned to probabilities. There's a certain (empirical) probability that a certain number of people will be bitten by a dog in a certain period of time, say one year. But the dogs do not consult statistical tables to work out when to bite and when not to bite! Despite this, probabilities have been assigned to such things. The probability of catching a particular disease, or how many years' life expectation. All these are based on past measurements. There is no theory, it's all experimental in such cases...until some bright spark discovers a theoretical explanation.