Although 'shogatsu' is originally another name for January, shogatsu often refers to a period from January 1st to January 3rd (sanganichi) or 'matsu-no-uchi (this period is originally through January 15th, but currently through January 7th for some people.)
「正月」とは、本来1月の別名だが、現在は1月1日から1月3日まで（三が日＝さんがにち）、または「松の内」（元々は1月15日まで、現在は一部では7日まで）を指すことが多い。