You will never have perfect results when visually comparing a Photoshop comp to a real program. In fact, it's not un-common for a text layout to be different between different computers because version and operating system differences (as well as monitor layouts) cause the text to reflow every time it's edited.
Unless things are very much different in other versions of Photoshop, your designer hasn't specified 32px because Photoshop doesn't lay text out in pixels - it works in points/picas. The exact text rendering is also dependent on the document's resolution (which is different between print and screen).
The best you can do is get the text to look roughly proportional to the designer's intent. In modern iOS, most apps will use the user's customized font settings anyway.