The word gooey is usually associated with something melted or something between a solid and a liquid. Gooey things are usually a little thick and slow moving. A good example would be melted cheese.
Sticky things are things that you might get stuck in. They hold to your skin or clothing. For example, if you spilled soda on a table, the table might become sticky later. Chewing gum, glue, honey, and syrup might also be considered sticky.
Hope that helps!