ITG has three general and non-exclusive playstyles: Stamina, Tech/FA, and Mods. There is an additional division with bar usage; generally people hold it on to it for balance in modern ITG, but no-bar is also common.
This video gives a good high-level overview of the different playstyles.
¶ Casual
¶ Stamina / Footspeed
The songs in the Stamina / Footspeed category aim to challenge the physical capabilities of the players through the length and speed of the songs. Stamina charts predominantly feature continuous streams with minimal tech or mods.
¶ Technical / Fantastic Attack
The Technical / Fantastic Attack playstyle challenges players to accurately play the chart while executing tricky patterns such as crossovers, footswitches and brackets.
¶ Mods
Mod charts challenge the player's reading abilities. Effects are applied to the arrows to make them more difficult to read.
¶ Doubles
A game mode/play style that uses both sides of the dance pad (8 panels) designed to challenge players' ability to accurately play charts that force the player to move across both pads.
¶ Couples
Couples charts are specially designed for 2 players. There is a noteskin that colors the arrows according to player. The players move across both pads.