Alpha and Beta of a Transistor
\$\beta\$ is a ratio between the collector and base currents whereas \$\alpha\$ is also a ratio but between the collector and emitter currents. There is no special name for \$\alpha\$ and \$\beta\$ as they are both unit-less.

However, you may call \$\alpha\$ as the common-base gain and \$\beta\$ as the common-emitter gain.

Either way, you will usually see \$\beta\$ in the spec sheets of BJT chips. 

\$\alpha\$ is always less that 1.0 because of carrier generation and recombination going through the base region of the transistor, thus, the base and collector current are always less than the emitter current.

There is a relationship between \$\alpha\$ and \$\beta\$... 

\$\displaystyle \beta= \frac{\alpha}{1-\alpha}\$

(Also, I asked a question about why Mathjax is different on the EE.SE than other websites.)