Medical PhD student here. In my Bachelor's Thesis, I used a publicly available dataset in order to test some hypothesis, different from the hypothesis the original authors tested. Before doing my analysis, I first tried to replicate the analysis of the original authors. To my surprise, although I could compute the same values for means and counts, I couldn't replicate their values for multivariate models. In the original article, the authors explained that they "controlled for factors such as age, gender and familial history", providing HRs and ORs only for the things they were interested in, but not for any of the cofounders.
What might be happening is that the original authors have not provided enough information about how they analyzed the data, thus making it very hard for others to "guess" the exact methods/models they used.
Moreover, different software (and different versions of the same software) can use slightly different methods/models/statistical tests. SPSS is a good example, newer versions using Lilliefors test instead of Kolmogorov-Smirnov for assessing normality. R also can use different types for sum of squares in ANOVA, while SPSS defaults to Type III (I think), without letting you choose. https://stats.stackexchange.com/questions/20452/how-to-interpret-type-i-type-ii-and-type-iii-anova-and-manova
In multivariate models, depending on the software used, different results can be obtained by simply choosing a different order for the predictors, or using a stepwise method instead of the enter method.
In genetics, depending on the protocols/machines used for reading DNA/RNA sequences, raw sequence data might contain "barcode" sequences that would be automatically discarded by the (proprietary) software used for data cleanup after reading, but you may not have this exact information or access to the cleanup software, while the repository requires authors to upload raw readings before cleanup. Different reference genomes might have been used (see HG19 vs HG38). https://www.thebiomics.com/research/human-genome-assembly/hg19-vs-hg38#:~:text=HG38%20includes%20additional%20data%20that,version%20of%20the%20human%20genome%20.
A personal beef of mine is with Brainstorm, which computes quantitative electroencephalography values based on EEG recordings. They don't provide an archive of past versions, and this year's versions have made significant changes to the interface, not only changing defaults but completely removing some options that I used last year in computing values. Essentially, I'm unable to reproduce past results using the only version available today. https://neuroimage.usc.edu/brainstorm/Introduction