The "past week" refers to the most recent week. If this is the fourth week of July, the "past" week would be the third week of July. The "last week" refers to the final week in a series. If the fourth week of July is the last, or final of four weeks of July, the current week would be the last week of July.

What does in the past week mean?

The most recent week, including today. (

What is difference between past week and last week?

I saw him last week. He married last week. in the last week refers to 7 days before the day in question for example if today is Sunday we count backwards. in the last week is used with present perfect tense or it can also refer to particular period of time in the future.