The Gladius was mainly a stabbing and thrusting weapon, Romans were taught to block behind their scutums and then thrust with a stab. They had a good understanding that even a wound a few inches deep in the abdominal area would often result in death or disabling their enemies from further combat.

But, according to Livy "Accordingly, those who, being always accustomed to fight with Greeks and Illyrians, had only seen wounds made with javelins and arrows, seldom even by lances, came to behold bodies dismembered by the Spanish sword, some with their arms lopped off, with the shoulder or the neck entirely cut through, heads severed from the trunk, and the bowels laid open, with other frightful exhibitions of wounds: they therefore perceived, with horror, against what weapons and what men they were to fight." http://www.gutenberg.org/files/12582/12582-h/12582-h.htm

Which could have also implied that gladius was used for hacking and slashing against the Macedonians.

As for your question, no the Romans did not use the gladius the same way long swords would be used if you are talking about what we could refer to as the clay more which was often wielded using both hands unlike the gladius which was short and made to be used with a shield.

As for different styles? I highly doubt it, there isn't much differentiating that you can achieve using a weapon made for stabbing. Just the basic block and stab. Although Romans did train with wooden weapons called Wasters which were heavier than the typical gladius as they believed that if you could train with a heavier waster than a real gladius would feel much lighter in combat.

Romans (or rather their gladiators) however, did have different fighting styles and techniques but that was often related to different weapons and armours and is an entirely different topic that I will not dwell into.