A welcome is a greeting that usually comes when you first arrive. Although you aren't fond of Aunt Martha, you always manage to give her a warm welcome when she comes to visit.
When you accept someone into your home courteously, especially upon arrival, you welcome them. When you visit your grandparents, they welcome you with open arms and a plate of homemade cookies. They might even shout, "Welcome!" when you walk in the door. Welcome also means to gladly accept. The president of the French club will welcome your fundraising idea, especially if it involves baked goods.