What is the difference between "unknown (and unknowable) initial conditions" and "uncertainty"? You can't go back in time to check the initial conditions.
The uncertainty in the initial conditions has no relationship with the "uncertainty" word used in the phrase "uncertainty principle", which refers to the relationship between the variances of two functions, one of which is the Fourier transform of the other.
I have refrained from using a phrase like "uncertainty in the initial conditions" and I have said "unknown initial conditions", precisely to not imply any connection with "the uncertainty principle", because no such connection exists.
Moreover, "uncertainty" is typically used about the difference between the true value of a physical quantity and its estimated value, but in quantum mechanics problems there are many cases when a value is completely unknown (i.e. all the possible values are equi-probable at the initial time, like the angular coordinate of the position of an electron bound in an atom) and not only uncertain.
Saying "unknown initial conditions" covers such cases.
