The most-noticeable difference between a snail and a slug is the slug's lack of a shell. On a snail, the shell houses and protects the visceral hump, where the snail's organs are located. A slug, on the other hand, may have an internal "shell," which is more like a calcium deposit, that helps protect the internal organs.
In addition to the shell, the two organisms also differ in their overall size and behaviors. Because the slug's size is not constrained by a shell, slugs can grow to be far larger than snails. Slugs are also more-maneuverable than snails and can generally fit into smaller and tighter spaces. This allows slugs to lay their eggs in safer and more-suitable places.
The snail and the slug also differ in how they defend themselves from predators. Generally, a snail will curl up into its shell when threatened. Due to their lack of a shell, slugs have had to develop other forms of defense, ranging from toxic or extremely adhesive slime to curling up their body tightly to make themselves more compact. While in this defensive posture, a slug will also excrete an extremely sticky slime in order to glue themselves to the ground which makes it harder for predators to dislodge the animal.