ik [I"k,Ik], ib and ip are not "types" of a fault but different current values in the case of the same fault [definitions of IEC 60909-0] :
Initial symmetrical short-circuit current I"k
peak short-circuit current ip
symmetrical short-circuit breaking current Ib
steady-state short-circuit current Ik
Usually an utility may transmit initial symmetrical short-circuit power S"k
and may be the System impedance at your connection point [or reactance to resistance ratio].
However "types" of short-circuit current could be:
line-to-line short circuit, line-to-earth short circuit, line-to-line short circuit with earth connection.