Different Print Page Dimensions Under Same Standard (A4)?

2 different reputable sources list 2 different A4 page dimensions: 8.27 x 11.69 and 8.27 x 11.7.

Furthermore, I have 2 different PDF resize programs. 1 outputs A4 files as 8.26 x 11.69, the other outputs files as 8.27 x 11.69.

Thus, among 2 different sources and 2 different programs, there are 3 different outputs for A4: 8.26 x 11.69, 8.27 x 11.69, and 8.27 x 11.7.

Why are there so many different outputs for A4, and which is actually the correct dimensions?

It is just because of rounding errors, due to how dimensions were computed, starting from A0, there are mathematical properties to define each subsequent format.

However the A4 standard says it is 210 mm × 297 mm with tolerances: ±2.0 mm for dimensions in the range 150 to 600 mm.

See the wikipedia entry: https://en.wikipedia.org/wiki/ISO_216#A_series

Now you seem to deal with inches (you did not say!), so 210mm is 8.26772 inches, which would round to 8.27 and 297mm is 11.69291 inches, hence 11.69 if rounded to two digits after the decimal. Of course that will be respectively 8.3 and 11.7 if you round to one digit only.