I have noticed that the Tosfos HaRosh very often parallels the Tosfos on the page. Sometimes he presents almost identical information in a slightly different way, but very often he seems to be saying the same thing.Please clarify. Thank you.

Definitely. The Rosh can be considered one of the latter day Ba’alei HaTosafot and accordingly, just like the many various versions of the Tosafot over the generations in Ashkenaz (like Tosfot Chachmei Anglia), they are often based upon those of Rabbenu Tam, the Ri, R. Shimshon MiShantz and the other classic Ba’alei Tosafot who precede them (including the Tosfot printed on the daf of Shas Vilna), with editing and additions of their own. It’s actually highly recommended to compare the different editions of the Tosfot on each masechta, especially when a Tosfot is difficult to understand, its parallel sources often help!