The ISO 8601 week
ISO weeks start on Monday and week 1 is the week that contains the first Thursday of the year. So the first days of January can belong to the last week of the previous year (for example 3 January 2021 is week 53 of 2020), and the last days of December can belong to week 1 of the next year.
Other systems
Some countries and software number weeks differently, for example starting on Sunday, so the number can differ from what you see in a US calendar. This tool always uses ISO 8601, which is the standard in most of Europe and in business and logistics.
Years can have 52 or 53 ISO weeks. To count days between dates, use the days between dates calculator.