Two systems, and why they disagree
The ISO standard, used across most of Europe and in most business software, starts weeks on Monday. Week 1 is the week that holds the year's first Thursday. So 1 January can belong to week 52 or 53 of the year before, and 29 December can belong to week 1 of the next.
The US convention starts weeks on Sunday and makes the week holding 1 January week 1, however few days of it fall in the new year. The two numbers often differ by one, and around New Year they can differ by more. If someone gives you a week number, ask which system. Usually it is ISO.