Just to be absolutely clear, the trip from Muir to the summit requires glacier travel experience and equipment, especially knowledge of crevasse rescue. It is technical in the sense that you must bring crampons, ice axes, ropes, snow and ice anchors, belay harnesses, slings, pulleys, prussiks or ascenders, and protection from high winds/cold/fierce sun. If all goes well and the weather holds it IS just a long, strenuous hike. But this doesn't happen all the time and some of the equipment mentioned earlier is often needed.
The trip to the summit is not for an inexperienced party, and the rangers might not let you go (they interviewed us many years ago, I assume they still do). On the other hand the hike to Camp Muir is just a long hike, easy route finding if the weather is clear.
As someone mentioned early, if the weather is bad be careful not to walk off a cliff onto the Nisqually Glacier. On my first hike to Muir many years ago we descended into a whiteout and couldn't see 50 feet. Route finding was difficult to say the least, and we really did worry about walking off a cliff!