The term "anomie" refers to a state in which society's norms and values have broken down. This leaves people feeling generally uneasy because there are no rules and values that are agreed upon by their whole society.
Sociologists talk of objective and subjective aspects of anomie. The objective aspects are those that can be put into numbers. For example, one might measure things like rates of delinquency or frequency of people moving to measure anomie. These measures might indicate the degree to which society is becoming unsettled and to which norms are breaking down. The subjective aspects are those that cannot be measured by numbers. These would be people's individual feelings. They would, for example, be things like the extent to which people feel like they have no purpose or the extent to which they feel like their society does not care about them.
So it is not so accurate to say that there are different kinds of anomie (subjective and objective). Rather, we should say that there are different measures of anomie.