There is only one portable playstation available in the market which is called The PSP. there are no other portable handhelds that are offered by Sony bearing the Playstation brand name.
The PS Vita is just a rebranding of the original PSP with some added features. For example,the Vita uses memory cards as a medium to load games on it when compared to the original PSP’s UMD discs.
From a buyers POV,its better to go for a Vita,as it has several improvements over the original PSP.