yes, the "common cold" can be carried by rhinoviruses, coronaviruses, influenza viruses (maybe a mild case of 'flu' mistaken as a cold), and adenoviruses.
this list is not comprehensive.
this list is not comprehensive.
From what I can find online, there's a correlation, but it's pretty light on details about how strong it is.
> Sense of "indisposition involving catarrhal inflammation of the mucous membranes of the nose or throat" is from 1530s, so called because the symptoms resemble those of exposure to cold; compare cold (n.) in earlier senses "indisposition or disease caused by excessive exposure to cold" (early 14c.), "chills of intermittent fever" (late 14c.).
Put less technical: shivering, runny nose, etc, are symptoms of both the common cold and being cold.