not necessarily - some plants drop seed and those seeds germinate the following spring, not in autumn, so depends on the plant.

To a certain extent it depends on what they are. Some plants have seeds with a very short life span and others can be safely stored until Spring. So Alliums, Primulas, Erythroniums, Trilliums, Aquilegia (all Ranunuculus family in fact) Hepaticas, Pulsatilla are better sown fresh. Dianthus can be kept until Spring.
Personally I always collect enough seeds to try all three methods, sown round the parent, sown fresh and kept dried and in the Salad compartment of a fridge until Spring and see what happens.