First, it is not the problem of a difference between the phrasal verbs "to go on" (to continue, to take place) or "to go for" (to go somewhere in order to have or get, to seek to obtain). The expresion "on holiday(s)" is similar to others like "in (the) Winter", "on weekends" or "twice a year". So "We go to the beach on holiday(s)" means we habitually go there in that particular time or season.
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