In very broad terms, there are 2 types of 911 systems in the USA.
Type 1 - Small system - perhaps just 1 or 2 dispatchers on duty in the
911 office - the calltaker also functions as the advice giver,
decision dispatcher, and radio dispatcher.
Type 2 - Larger system - the first person who answers the 911 phone
call is a police calltaker - if the call requires fire or ambulance
service, the police calltaker transfers the caller to a fire and/or
ambulance calltaker
(Type 3 - I think that New York City is using an alternative system -
the first calltaker takes the info from the caller - and forwards the
INFO to a decision dispatcher or radio dispatcher)
(Type 4 - I think that San Francisco is using an alternative system -
each calltaker serves 1 neighborhood - and also serves as the decision
dispatcher and the radio dispatcher for that neighborhood)