Is the brown discharge that appears at the time of menstruation, accompanied by menstrual pain, considered menstruation (hayd) that necessitates breaking the fast, or irregular bleeding (istihadah)?

The fatwa (definition) we follow is that brown discharges (kudrah) are considered menstruation if they occur at the time of menstruation or are continuous with blood. What you did by breaking your fast is correct if these discharges continued for a day and a night (the minimum duration of menstruation according to the majority of scholars). However, if they stopped in less time than that, they are not menstruation, but rather istihadah (definition) (non-menstrual bleeding).