There are 6 different styles of playing Twoccer World, and they can be played normally (World Mode) or with the option of using 2 abilities you've learned (Ability Mode). Your goal is the same in all 6 modes, gain as much score as you can before your timer runs out.
Original
Play by normal rules, steal items to generate clocks, which give you more
time. Gems and Tomes can be stolen to give beneficial effects to help you.
Timed Twoccing
You have a fixed 3 minutes in this mode to rack up as much score as you can.
There are no clocks in this mode.
Gem Grabbing
Clocks give you less extra time in Gem Grabbing, but there are more gems than
usual to give you the advantage back.
Tome Taker
You start with 1 of each Tome in this mode, and can collect up to 5 instead
of the default 3. Like in Gem Grabbing, clocks give less time to counter this.
Relay Robber
Items are worth just 1% their usual value in this mode. Instead, the locations
of 3 batons are marked on your map. When you collect one, another will replace it
elsewhere. Worth a lot of points, it is these that will give you your score.
Though you can't ignore the worthless items completely as you'll still be
wanting clocks to appear.
Stupid Mode
There are far more roaming items than normal in this mode, it takes longer
for a clock to appear and to level up to balance this.
Mission Mode
Each mission requires a specific task to be completed. Unlike World Mode and
Ability Mode which are based on how much score you can get, your success in
Mission Mode is based on how quickly you complete the mission. Like in Ability
Mode, you can equip 2 abilities to help you finish the mission as quickly as
possible to try and get the highest grade.