forward and backward error

Question

Hello I am a bit confused on the forward and backward error for floating point computation inaccuracy. Let s take only the absolute values. I understand that the forward error is the difference between the result and the solution. The backward error is smallest Δx such that f (x + Δx) = y*; in other words, the backward error tells us what problem the algorithm actually solved (per wikipedia). By researching also I read that the Backward error is more stable. Does this also apply when I search the absolute value? Because only thing I could find was for the relative error. However how am I supposed to choose between choosing forward or backward error for numerical purposes for absolute values?