Free Running Counter : A counter is said to be free running if it contains all possible states in the counting loop.
Self Starting Counter : A counter is said to be self starting, if it is possible to enter "counting loop" irrespective of initial states.
With 2 bit we can count maximum 4 number i.e mod 4 counter is possible, so above example is free running counter
Here we can enter into loop irrespective of initial state, thats why its self starting counter as well.
Here is another example
With 2 bit we can count maximum 4 number i.e mod 4 counter is possible, but here its mod 3, so its not free running counter
Its not self starting as well, since if we starting at 00, we never going to enter a counting loop, we are going to stuck at 00.