Good question. The main difference is the sport, which changes the modality a bit.
Let me clarify: Josh’s plan prescribes the training modalities of rock climbing, bouldering, and fingerboarding plus some optional workouts for mobility/stretching and running. The focus of this plan, being more cragging/rock climbing utlizes rock climbing as the main modality so as to train those key muscles, tissues, and joints between the fingertips and shoulders.
My 5-week plan was written specifically as a transition period plan for my 8 week Advanced Rock Alpinist Plan, which as it states, is pretty advanced and many people would end up injured if they jumped straight into that. The 5 week plan has as an average week: 3 runs, 2 gym strength sessions, and 1 climbing day. So less of a specific rock climbing focus, as an alpinist needs a very large base of aerobic support for the aerobic nature of the activity which involves appraoching/climbing/descending, not only simply pulling down.
Honestly, I think either plan would accomplish a good base of support for your ice climbing training. One is weight gym based and one is climbing gym based. But they do the same thing in the end. My 5-week plan is 5 weeks because the 5th is a taper week intended to de-load you (allow for rest) before starting the 8-week advanced rock alpinist training plan.
I hope that helps clarify this for you. Let me know if you have further questions.