Stretchy T-shirt yarn stretches and bounces back into shape. Stiff T-shirt yarn has very little give. That difference changes the final feel, and it also affects how stable edges and bases are. For baskets, the stiff type tends to hold straighter sides. For bags, the stretchy type can give under the weight.
A good T-shirt Yarn Book explains how to choose the right type depending on the project. It should also mention making a swatch or test piece—when you’re working with T-shirt yarn, that prevents surprises with sizing. If you’re going to buy T-shirt yarn books, look for ones that explain substitutions. They should tell you what changes when you vary thickness and stretch.