In monostable, how long we trigger is the trigger time. If I trigger it for 10 minutes then during this time I get output high.
"Trigger time" is not an expression that we use. We can talk about the trigger pulse's width or duration, or its repetition rate.
Generally, the trigger pulse to a monostable should be very short. In some designs of mono, such as one using the 555, the output will remain high if the trigger remains low.
Others, such as the two-transistor cross-fed monostable, would not repsond until they receive another transition, of the correct polarity, at its trigger input.
"Trigger for 10 minutes" would indicate, unless you state otherwise, that the monostable is receiving a series of pulses over a period of 10 minutes, not a single pulse of 10 minutes duration.
The duty cycle of an astable is designed into it. We design it to have a know repetition rate (frequency) and a known duty cycle. We apply power and it gives us pulses at a known frequency and of a known duty cycle.
We can't design that into a monostable. Switch it on and it does nothing. Apply a trigger pulse and it produces a single pulse of known duration. That's all.
Nor can we design a duty cycle into a bistable. Switch it on and it does nothing.
Apply a pulse to its set input and it changes state. That'all. It doesn't produce a pulse. It then sits there doing nothing ... unless or until you apply another pulse, to its reset input, whereupon it revertsto its original state.