The term bestiarii does actually have some ambiguity in Roman terms, with almost two separate meanings for the term. The first meaning is that the bestiarii were men who fought animals in combat in the Colosseum, and not really gladiators, as that term typically refers to someone facing another man or woman opponent.
A cestus or caestus is an ancient battle glove, sometimes used in pankration. They were worn like today's boxing gloves, but were made with leather strips and sometimes filled with iron plates or fitted with blades or spikes, and used as weapons.
Dimachaerus. The dimachaerus (Greek διμάχαιρος, "bearing two knives") used a sword in each hand. Equites. Eques, plural equites, was the regular Latin word for a horseman or cavalryman. Early forms of the eques gladiator were lightly armed, with sword or spear.
The murmillo gladiator was a very general type of occupant in the Colosseum due to their standard weaponry and shield. They were initially created as a gladiator class when the relations between Rome and the Gauls at the time grew more fruitful.
A retiarius (plural retiarii; literally, "net-man" or "net-fighter" in Latin) was a Roman gladiator who fought with equipment styled on that of a fisherman: a weighted net (rete, hence the name), a three-pointed trident (fuscina or tridens), and a dagger .
A secutor (pl. secutores) was a class of gladiator in ancient Rome. Thought to have originated around 50 AD, the secutor ("follower" or "chaser", from sequor "I follow, come or go after") was armed similarly to the Murmillo gladiator and like the Murmillo, was protected by a heavy shield.
The Thraex (pl. Thraeces), or Thracian, was a type of Roman gladiator, armed in the Thracian style with small rectangular, square or circular shield called a parmula (about 60 x 65 cm) and a very short sword with a slightly curved blade called a sica (like a small version of the Dacian falx), intended to maim an opponent's unarmoured back.