Fullness and satiety are definitely related but distinct concepts and sensations when it comes to food and nutrition. 

Feeling " full" is physical and mechanical sensation triggered by the stomach having expanded. Some express it by loosening their belts, some say they feel "stuffed"
It's short term and results in feelings of hunger. 

Satiety is complex; it is a result of efficient hormonal signaling that activates the psychology that governs eating behaviors. 
It's responds to quality, quantity of the food ingested and is long term. 

Meals that leave you wanting more, especially if there's room for dessert, are generally filling but lacking in satiety. 

Meals that leave you feeling satisfied with no further need for food, especially dessert, are generally nourishing and satiating.
You can have dessert, only if you want to.

True satiety is about having a nourishment without feeling 
"stuffed" ; but you can feel "fullness" and be satiated with a pleasant feeling of "enough"

You can leave the table thinking and saying "that was a good meal"