well... to state the obvious...
VTIAX invests in international companies. VTSAX invests in all publically traded US companies.
VTIAX has higher fees because it costs slightly more (on average) to invest in foreign companies.
It's up to you to determine how to invest. many people are 100% VTSAX (note that roughly a 1/3 of all profits from VTSAX come from these US companies selling stuff overseas). Others want more international exposure, so they add VTIAX.
What you do is up to you, your comfort level, your expectations for the global economy over the next 10, 20, 30 years... etc.
hope that helps.