No no they are not, which to choose depends on both the data and what you are asking, in short;

Conditional logit - the preferences are homogenous and the independence of irrelevant alternatives is reasonably just

Mixed logit - preferences are ~ heterogenous and IIA is relaxed/does not hold

Dear Marius Ole Johansen Thank you so much. This brief and bold answer helps me a lot. Will wait in this platform for further discussion and STaTa commands suggestions from other scholars in this network ahead.

Conditional logistic regression is an extension of logistic regression that allows one to account for stratification and matching.