They are structurally similar but differ in their 3D dimensional form. 

Beta isomer means above plane and alpha isomer means below plane

 i agree with Shubhangi Soman ·

the α isomer has a carbon-carbon double bond inside the six atom carbon ring, while in the β isomer, the double bond is outside the ring, or can say that depend upon the location of double bond.

Bs Rawat, you are definitely right. Still I wanted to know why scientists designated them alpha and beta.

Same answerer has already given by many scientists its terminology to differentiate the two and given by standard IUPAC

They are constitutional isomers (same molecular formula but different chemical structures) They differ via the position of the alkene (internal in alpha, terminal in beta).

Thank you all.

I guess alpha pinene was isolated first, and later when its isomer was discovered, it was named beta-pinene, thus the initially isolated pinene has become alpha. 

By the way, alpha and beta descriptors in this case have nothing to do with traditional stereochemistry notation (down/up). Anyway, it is not always easy to find logic in the naming of natural products.

Thanks Dr Vladimir. I think your answer covers all the confusion regarding this naming.