Question

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

Answer 1

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.

Answer 2

The red laser will have a hotter temperature than the blue, so it is red because it is hot
hope this helps!!!