Common Army Phase, as the name suggests, is a requirement for all army officers. Additionally, some officer candidates in so called "green" air force trades are required to take it (from what I have seen, air force construction engineers as well as air force MP's). Regardless of occupation, all officers take the same CAP course. CAP (R) is for reserve officers. As for the slight discrepancy in course length (8 vs.9 weeks), the Combat Training Center likes to put on a big parade with all the graduating officer courses at the end of the summer, and a week's practice is usually set aside for that.
Keep in mind that it is the Infantry School that runs this course, and they consequently have the most up to date information. The officer training system has been in flux for the last couple of years, and there have been a lot of misunderstandings as a result of this.
Just to clarify a couple of nomenclature points, there are two resources that you will find on the DIN that are most useful. Firstly, there is the Course Training Plan (TP). The TP describes performance objectives, and provides an rough timetable for the course. Secondly, the course will have a set of Master Lesson Plans (MLPs). This is the actual "meat" of the course material and is a good pre-study resource. Many of the MLPs will even have handy powerpoint slide presentations with them.
Just as an addition to chaos75's post, yes this is a fun course that you will probably find quite rewarding.
By the way, did you find the Infantry School joining instructions O.K.?