Without knowing more details about the calculation, most likely it is a result of differences in BLAS/LAPACK (the libraries used for dense matrix multiplications and matrix decompositions).
What version of BLAS/LAPACK are you using? You can find out with `using LinearAlgebra; BLAS.vendor()`. The same BLAS/LAPACK library may have different implementations on different systems.
However, if floating point discrepencies are leading to very different results, you may want to rethink what you are calculating and how you are calculating it, since it sounds like what you are calculating may be very small or very large. Could you provide some details about what you are calculating?