Good question. There is a large area of overlap. Gather has the sense of bringing together in one place while collecting refers to picking up in sequence. You can gather 'round the Christmas tree or attend a family gathering. In dressmaking, gathering refers to a bunching together of fabric. You would collect a number of individuals by car destined for the same location. You could, however, both gather or collect your senses or wits. If I say, "Gather your things, we have to leave," the emphasis is on getting them all together. If I say "Collect your things" the emphasis is on going and finding them one by one, at least to my thinking. It's a subtle difference, and in many cases they are interchangeable.
You can also check: https://wikidiff.com/gather/collect
