Best practice for computing week-over-week change in MAU metric When we calculate week over week change for a metric like "Monthly active users", we often refer to a calculation of SUM(This week) - SUM(Last week)/SUM(Last week), which means we will run total of this week's number first, and then compare to the total from last week. 
There is another situation when we can have change any date comparing 7 days ago(week), So each date during a week will have a change value.

Are there any best practice for this "week over week" concept. I've also heard that someone is using "weekly change" referring to the similar thing. Is there any difference? Which calculation I should chose?
Both of these options have value if interpreted properly. You are trying to answer  the question (I assume): 'are we doing better this week than last week?'

I don't know what industry you're in or how variable (or volatile) your metric is, but I'd advise caution in interpreting changes week to week. I might suggest that alongside your weekly (or whatever) metrics, you include some moving average. That way, you capture the overall trend while tempering your reaction to occasional ups and downs.