I discovered just this week that the numbering of weeks within the year is different between US and Europe, thus, cal -w can show different numbers for some years depending on the locale. Outlook can probably also show different things depending on the system settings.

Europe uses the algo according to the ISO 8601 standard, where the week no.1 is the one with January 1st occuring between Monday and Thursday, inclusive. If the 1st happens on Friday or later within a week, it's considered a week no.52 or 53 of the previous year.

US does not use this scheme and [EDITED] I am not sure what method is applied there.

Some companies use week numbers in business talks, planning and scheduling, so be aware who is speaking about which weeks!

Even the concept "within that week" depends on whether you consider the week to begin on Monday or Sunday. (or elsewhere I suppose)