If a language L is generated by a regular expression, then L is recognized by a DFA.
I think this is true, because regular expressions describe regular languages, those of which are exactly accepted by DFAs.
If a language L is recognized by an NFA, then L is generated by a regular expression.
I think this is true as well, because all NFAs are DFAs, and the class of languages accepted by DFAs are regular languages which can be expressed as regular expressions.
Am I confusing any topics here? I'd appreciate any clarifications or intuitive explanations if my understanding seems wrong.