A portable mortgage, where available, is one that you can carry with you when you buy your next home and avoid paying any discharge penalties. This means that you will not have to go through the entire mortgage process again unless you are making a move up to a much more expensive home.
An assumable mortgage is one that the buyer for your home can take over when you move to your next home. This can be a very powerful tool at the negotiating table, making it much easier and more desirable for a buyer to buy your home, and again saving you any discharge penalties.