You do want to report both accounts on your FBAR, since the value was in each of them for a time. However, for purposes of determining whether or not you need to file 8938 those amounts aren't added together.
FBAR requires you to report the highest value in every account you had open at all during the year if at any time you meet that filing threshold ($10,000 USD equivalent). When money is moved from checking to savings or between banks it can make it appear as if the individual has more money than they actually have, but FINCen is aware of this nuance.
For 8938, the threshold applies only if you had more than $50,000 of total assets on the last day of the year or $75,000 on any day of the year (for single filers living in the US). However, this is using your total value of real assets, and doesn't require combining values when you move funds from one account to another.
The full list of reporting thresholds by filer type can be found HERE.
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