So you may be surprised to hear that there are 8 distinct and different types of timer. The 555 can do some of these - but not all. A gives a positive going timed output pulse when it is triggered. B gives a negative timed pulse when triggered. C goes positive after the trigger event, delayed by the time period.
D goes negative at the end of the delay period.
The second column shows the equivalent four timers, but now reacting to a negative going edge. The three 'important' timers, for industrial control purposes, are shown with a red dot. A gives a positive going, timed output pulse, triggered by a positive input edge. C's output goes high after a timed period, with the timing triggered by a positive going input. The second column's C goes low, delayed, after a low going input.