For yogis looking to modify their chaturanga as they’re building upper body or core strength, I know of two main variations: using a wall and dropping the knees.
Chaturanga at the wall basically involves rotating the pose 90 degrees. Instead of lowering from plank down toward the ground, one would move oneself sideways toward a wall, sort of like this:
Chaturanga at the wall changes the body’s relationship to gravity. Here, while the core and shoulder muscles are definitely engaged, they’re not working as hard to actually support the body. This can be useful for building up strength or for exploring alignment in the pose. For instance, I use chaturanga at the wall to really let myself look at my upper body: to watch whether I’m sliding my elbows back out of alignment or whether I’m dropping my shoulders below my elbows. When I’m not working against gravity, I can easily correct if I move too far, and I can also hang out in the correct alignment for a while to give my body and brain a chance to remember what “right” feels like.
I find using the wall very informative for focusing on chaturanga in isolation. Unfortunately, it’s not so practical in the context of a traditional sun salutation. For that, lowering the knees is probably a handier alternative:
(Video from Yogatic via YouTube.)
Effectively, placing the knees on the floor changes the amount and distribution of the weight the shoulder and core muscles need to support. Placing the knees directly under the hips maximizes the weight held by the lower body (and/or the floor) while sliding the knees back gradually moves more of that effort to the core muscles.
Chaturanga variations are important, first and foremost, for safety. It’s no fun injuring a joint on account of asking too much of muscles before they’re ready. And just like every chaturanga expression isn’t right for every yogi, neither is a single expression right for every sun salutation. For instance, in my practice, I like to start with me knees down until I’m sure that I’m warmed up and pain free on any given day. And I’ll only stay with the knees up version of the pose as long as it’s enjoyable for me. If I’m saving my upper body strength for something like arm balancing later, it makes sense to me to put my knees down for chaturanga earlier and more often.