These terms all refer to a kind of reptile that has a long, thin body and large, fanged jaws, and that moves by slithering back and forth across the ground. The term "serpent" usually refers to a large snake and "viper" refers to a type of snake that has venom which it uses to poison its prey.
* After the serpent tempted Eve to sin, and both Eve and her husband Adam did sin, God cursed the snake, saying that from then on, all snakes would slither along the ground, implying that before then they had had legs.