In general terms, TSI engines are petrol-powered whereas TDI refers to diesel motors. Specifically, TSI stands for Turbocharged Stratified Injection and refers to the combination of turbocharging and fuel injection VW uses to improve both power and efficiency, the technology having evolved over the years.
Likewise, TDI, which stands for Turbocharged Direct Injection, is branding for equivalent technology in diesel engines. This again has been around for some time and developed over several generations of cars. In more modern models you may see an additional, lower case ‘e’, which usually indicates some manner of hybrid assistance.