With a square, the basket will now rest on its corners and the center of the base is lifted off the table. With both, the weight of the basket will be distributed to the outside edges. The inside will be slightly raised up. In other words, if you put marbles in your basket, they'll roll to the outside edge. These are the three interchangeable names for the same part of the basket structure.
Weavers are strands that go over and under the spokes to complete the basket.
It's also the very same pattern that you wove when you made paper placemats in Kindergarten. As a beginner, sometimes I can't tell if I've made a mistake. Simply backtrack along the row, looking for the error. The break in the pattern will be easy to spot, and you simply unweave the basket to that point and continue again. Tension in basketweaving, I tell my students, is like tension in knitting or anything else.