What is the difference between bio and genetic engineering?

is the application of engineering principles to address challenges in the fields of biology and medicine

Genetic Engineering is the manipulation of gens.

Bio is all aspects of life - medicine, pharmaceuticals, biomechanics, etc.  Genetic is specifically dealing with genes.

For example, the genome of a lab mouse might be used in genetic engineering to track down a gene for a particular disease (i.e diabetes).  The genomes of those mice with the disease would be compared to those without it, and differences noted.  If this special gene that causes a disease is isolated, then ways to prevent it from functioning might be developed, and turned into something useful for humans.  That's genetic engineering.

A lab mouse in bioengineering might be used to grow an ear on its back (actual experiment), or have a mechanical arm attached and figure out how the mouse can use its brain to control the circuits and motors that move the arm.  Or maybe the mouse is used for testing a new synthetic drug to see what it does.  These are bioengineering.  Bioengineering would generally include genetic engineering as sub specialty.