The sad fact here is that "earnings" on the numerator can be measured in a multitude of ways. The "per share" should be consistent (although these can differ a little, depending on whether one uses the year-end vs the year-average share count).
More normal is the variation across different "E" figures. First of all, you need to make sure that one is not reporting the last quarter's results, while the other is reporting the rolling L12m, ie the sum of the same over the last four quarters reported.
Even assuming consistent time-horizons, the "E" can differ, depending on the source. There is GAAP accounting (or IFRS outside the US), which is the headline number reported in the company's accounts. The issue here is how one deals with one-off "exceptionals" that are not represntative of the company's underlying true profitability. So you have an "operating EPS" that strips out below-the-line one-off exceptional charges or gains. And then you have "adjusted EPS" that is the analyst community's opinion on what the true repeatable profits were and will be, both being comparable to each other.
Each has its strengths and weaknesses. The bottom line is that there are multiple "E" numbers on the numerator out there. Profits being an accounting opinion, from first principles.
The trick here is to be very clear exactly what one is looking at in each and very such measure,