When we in NYC talk about 'the Holidays', we mean the period from late November to New Year's Day.
'Holiday' in the singular can refer to anything from Easter to 'Talk Like a Pirate Day', depending on the person.
'Vacation' usually means a trip of at least a week away from your home base. As I understand it, the term came into being during the 19th century. During the hot months, wealthy people would close down their town houses. Women and children would be sent off to cooler, relaxing places such as the Catskills or Eastern end of Long Island. men continued to see to business. During the week they boarded at their Clubs and visited their families on the weekends.
This was the time that major repairs and cleaning could be done to the city house without discomfort to the family. Because the house was vacated. The summer became known as 'Vacation' and the term filtered into general use.