Umbrella words are informal ways in semantics of naming a generic term (hypernym) that covers several specific or subtype words (hyponym) which are related in meaning.  Wikipaedia explains that for example, pigeon, crow, and hen are all hyponyms of bird and animal; bird and animal are both hypernyms of pigeon, crow, and hen. 
Linguistics is the overall study of any  language. All languages are studied according to their grammar ( word structure and word form), pronunciation (sound system) and  semantics (word meaning).
So one could also say that Linguistic is the hyponym or umbrella word for grammar, phonetics and semantics.