Well, both VTEC and VVTi -as well as their many flavors are the same basic thing in principle. The only differences are minor and relate to the implementation.
VTEC achieves this by switching between two different cam profiles, and thus can switch between two (or even three) sets of valve timing and duration profiles. The direct equivalent of this system is actually the VVTL-i, not VVT-i. (VVTL-i can change the lift and the timing just like VTEC can. However Toyota has stopped using this system because of emissions problems.)
The regular VVT-i system relies on changing the rotational relationship of the camshaft to the crankshaft by varying a mechanism within the drive end of the camshaft, and Ahmad Bhai is correct in the plain VVT-i does not change the lift of the valves, only timing. However, this system has an advantage over VTEC in that the timing can be changed very smoothly, instead of abruptly switching cam profiles.
Thus, VVT-i does not have the same "kick" that VTEC is famous for, but the improvements in performance are very similar.
Both systems have many variants, and can be found on one or both sides of the engine. The links supplied above by Fahad are very good reading.
I can answer more questions here if there are any, but with the OPs specific permission. 
