The confusion arises when discussing whether Cruz was a citizen at birth or not. There are two ways to be a citizen, by birth or naturalization. When children born abroad have citizenship transmitted to them by their parents, it is called by birth even though an overt action must be taken to get the citizenship. It is called citizenship at birth even though someone could wait until any age to apply for it. The "by birth" distinguishes it from citizenship by naturalization.
Cruz was a dual citizen until May 2014 when he renounced his Canadian citizenship.