It is uncommon for a paper to be accepted for publication without changes – most papers are revised at least once in light of comments from reviewers and editors.
When a revised paper is received:
Ideally, any significant changes should already have been requested in the original review – this subsequent review should be to ensure that the changes have been made, rather than for raising additional issues.
Thus your review of a revised manuscript should be relatively quick and may only involve checking that certain requested actions have been done. Nevertheless, the aim of the review remains the same: to ensure the paper is of a publishable standard.
Usually the editor will provide both the original decision letter and the author’s response to it. This will allow you to see what changes were requested – including any by the other reviewer – and how the author has responded to those changes.
You should focus on how the author has changed the paper in light of their own response comments. Some journals require authors to highlight the changes in their revised manuscript, which simplifies this.