I understand that there are two types of tefillin, the standard Rashi, and Rabbeinu Tam's. How do they actually differ in construction and in makeup? I have heard that the scriptural passages are arranged differently, but are there any other differences?
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The main difference between them is the order of the passages: whether "Sh'ma" appears before (Rashi) or after (Rabenu Tam) "V'haya im shamoa". An additional difference is that, in the head t'fila, the parchment containing "V'haya im shamoa" is wrapped in a hair that sticks out the front of the t'fila, and where that sticks out identifies at a glance the order of the passages within.
Source: e.g., Rabbi Shimon Eider.