what are the differences between "past week" and "last week"? [closed]

What are the the differences in meaning between the following phrases:

past week

And

last week

Please try to explain it with as many examples as possible!

The difference is "past week" would be to count back exactly a week from now, while "last week" is the calendar week preceding the present week. "Past week" is usually used when going through something/event. "Last week" is usually used to point to that particular week.

Example:

For the past week, it was raining heavily.

Last week, it was raining heavily.

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.

"Last" week can be used for the "past" week, if the implication is that the "past" week" is the last of all weeks up to now.

The converse is not necessarily true; the "past week" cannot generally be used to describe the "last week." Unless we were in say, the first week of August, in which case the "past week" would describe the "last week" of July.