I agree with the mathematical proofs that 0.999… = 1. However, I also feel like there is a theoretical difference between them, no matter how infinitely small it may be.
For example, if you have have 2 points on a line, point A and point B, and they are 1 unit of distance apart. If point A moves 90% of the distance towards point B, it has travelled 0.9 units. Now if point A travels 90% of the remaining distance toward point B, it travels 0.09 units. So now it has travelled 0.9 + 0.09 = 0.99 units. Continue travelling 90% of the remaining distance and infinite number of times (this becomes a geometric series if I understand them correctly). However, point A will never travel 100% of the remaining distance and will therefore never travel exactly 1 unit of distance and will therefore never reach point B.