Search for any areoles on your plant. This is a defining feature of a cactus as it is very specific to this plant. An areole has two buds that are opposed to one another. From the top side an offset shoot with flowers can emerge, while spines and hair appear from the lower bud.
Cut a small piece off the limb of the succulent plant that you have and note whether it is fleshy on the inside. The limbs may be ribbed as well.
Study the roots by lifting the plant out of the pot with a folded piece of newspaper. Note whether there are many shallow feeder roots and if they spread out. Since cacti live in desert conditions their roots are short and spreading in order to collect as much water as possible in a very short time.
Study the plant stem. Cactus skin is waxy and the spines act like funnels that channel water to the base of the plant so the roots can soak it up.
Check whether your plant has leaves or spines. Cacti have spines that come in a variety of shapes and sizes. They can be straight or crooked, long or short and even soft or pointed --- and can come in different colors. They may look thorny but they are not thorns.