First of all, they are both reptiles. They are from one and the same taxonomy order in the reptiles classification. So they come from Kingdom: Animalia, class: Reptilia and Order: Testudines.
But then you go further and understand that their family, genus and species levels are different. Their common trait is the hard protective shell both animals have. As they are quite slow animal they use their shell to protect themselves from predators. They are also both egg-layers and ectothermic, as they use outside sources like the sun to warm their bodies.
What Makes Turtles and Tortoises Different
The primary difference is that scientists classify tortoises and turtles in different "organization". Also there are other differences.
Tortoises are land-dwelling animals which eat low-growing vegetation. They are larger, heavier and bulkier than turtles. Also their feet unlike to these of a turtle, are stubby with sharp claws for traction.
Tortoises cool their bodies underground burrows and warm it from the sun. Turtles live in or near water. Their feet are webbed in order to swim well. They are more streamlined and use water to cool and the sun's rays to warm themselves.
First of all, they are both reptiles. They are from one and the same taxonomy order in the reptiles classification. So they come from Kingdom: Animalia, class: Reptilia and Order: Testudines. 
trait is the hard protective shell both animals have. As they are quite slow animal they use their shell to protect themselves from predators. They are also both egg-layers and ectothermic, as they use outside sources like the sun to warm their bodies. 
The primary difference is that scientists classify tortoises and turtles in different "organization". Also there are other differences.
Tortoises are land-dwelling animals which eat low-growing vegetation. They are larger, heavier and bulkier than turtles. Also their feet unlike to these of a turtle, are stubby with sharp claws for traction. 