Why does laser beam might appear blue and another laser beam might appear red?

A laser emits light at one single frequency (one single wavelength). 
But not all lasers emit the same one. 

The frequency (wavelength) that comes out of a laser depends on the
material that's doing the 'lasing' ... different material fabricated into a
laser diode ==> different wavelength in the output.  

Many lasers, but not all, emit a frequency (wavelength) that's in the visible
range, and a single given laser may emit red, orange, yellow, green, blue,
or violet light.  Lasers of other designs emit at frequencies outside the visible
range, in the microwave, infrared, or ultraviolet.