The name Basil comes from Greek and means Royal Plant. There are many varieties of Ocimum basilicum. The type used in Italian food – and in many drink recipes - is typically just called basil, sweet basil or Genovese basil, as opposed to Thai basil which is much different with a more anise- and licorice-like scent and taste, or lemon basil with its lemony teste.
Often you want to boost the scent from your basil or any other fresh herb – the only thing you need to do is to give it a squeez. If you need more flavors you simply just give it a good smack and the difference is significant. But be careful that it is not overpowering the drink!