As [MENTION=106176]wfo9[/MENTION] stated, they are similar in principle, but have different approaches.
VVTi (Variable Valve Timing Intelligent) physically alters the valve timing by moving the camshaft sprocket, thus advancing or retarding the entire camshaft X amount of degrees as determined by the ECM.
Where as VTEC actually changes the camshaft profile (changing timing and lift), The way most VTEC systems work is that the ECM locks the rockers to a 3rd more aggressive cam lobe.
(I have no idea why they call this Toyota VVTi because this is Honda VTEC...)
Toyota has recently taken a page from BMW (unfortunately) and started implementing on some engines "ValveMatic" (sounds very similar to BMW's ValveTronic...) that uses both VVTi and a 3rd camshaft to increase the lift and duration of the valves opening while also adjusting timing.
I'm not entirely sold on the new ValveMatic system as it seems to be heavily borrowed from BMW's shelf and the issues they have/had with them have made me wary. The concept is sound though.
And for shits and giggles, here's the "future" :
Because THAT isn't gonna have problems with how often solenoid failures seem to happen in modern vehicles. :bored: