The Samaritan Pentateuch is the Torah as the Samaritan community has it, written in this alphabet, and it differs from the Masoretic text used in Judaism in a very large number of places. Most of the differences are small: spelling, the presence or absence of a vowel letter, a singular against a plural, a smoothed grammatical form. A smaller number are substantial, and a handful bear directly on what divides the two communities.
The clearest of those concerns the mountain. The Samaritan Pentateuch names Mount Gerizim as the place God chose, where the Masoretic text does not, and the Samaritan version of the commandments carries an instruction to build an altar there. Elsewhere the Samaritan text expands a passage by bringing in wording from a parallel passage in another book, which produces a fuller and more internally consistent Torah.
Two facts about that pattern belong together. The differences are catalogued, published and open to anyone who wants to check them, so this is not a matter of rumour. And a substantial share of the Samaritan readings agree with the Greek Septuagint against the Masoretic text, while some agree with manuscripts found at Qumran, which means the Samaritan text is not simply a later alteration of the received Jewish one but a witness to how the Torah was circulating before either tradition settled.
Which text stands closer to an original is a live scholarly question and a matter of religious conviction for two communities. The atlas records the differences and does not adjudicate them.