The term "outdoor fireplace" covers everything that creates heat on the patio. This can be in the form of a pit, a hearth, a ring, or the traditional chimenea. It does cover the big fancy built-ins, too. Choosing an outdoor fireplace among the many offerings isn't easy.
Those with single openings (chimeneas) will produce concentrated heat at the front. Select a large bowl so you'll always have plenty of fire. Taller chimneys will whisk smoke way better, too.
Firepits with full-surround viewing are best for ambience as everyone can gather around.
Clay pots are easily breakable. They also deteriorate over time, too.
Cast aluminum is lightweight and great for home use. If you're afraid someone with sticky fingers will cart it away, choose the heavier cast iron version.
For more details, read about Outdoor Firepit Types here.