Well based upon the information that you have provided, Deathstroke the Terminator Vol. 1: Assassins was written by Tony S. Daniel - probably best known for his Batman comics - and illustrated by Sandu Florea. "...[W]hen Slade is betrayed by his trusted friend and left for dead, the world thinks Deathstroke has finally been eliminated.... Now, Slade has awoken with a completely new... mission: find the man who arranged his death, and who is building an army that will threaten every nation on Earth" (from the back cover of the TPB).
Volume 1: Legacy was written by Kyle Higgins - best known for his Nightwing comics - and illustrated by Joe Bennet. "Deathstroke's tactical prowess is put to the test when the man who hired him attempts to renege on the contract" (from the Amazon description).
As you will notice, these comics were created by different teams and they focuses on different stories. Moreover, Daniel's series came out in 2015 and Higgins' is from 2012.