# Multinomial Model of Discrete Choice

Can anyone explain me the differences between Multinomial Logit Model and Conditional Multinomial Logit Model?

Multinomial Logit Model $$P(y_n=j|z_n=z)=\frac{exp(z'a_j)}{1+\sum exp(z'a)}$$

Conditional Multinomial Logit Model $$P(y_n=j|x_n)=\frac{exp(x_n'\beta_j)}{\sum exp(x_n'\beta_j)}$$

The ordinal logistic regression is also a multinomial model?

I'm using this reference Categorical Data Analysis, Alan Agresti, if anyone has another references I appreciate.