The board is correctly set as MKR1000. But when I select the correct port the port designation is: \dev\cu.usbmodem1201 (ARDUINO MKR WIFI 1010) (on a MAC OS). It is also curious that the function for the board information is showing: BN: Arduino MKR WiFi 1010.
Ignoring that and going to the WIFI Updater, ist is only showing the NINA firmware updates for MKR WIFI 1010. Of cause the update fails if I try to install it.
With the MKR boards, if you accidentally have the wrong board selected from the Tools > Board menu and do an upload, it will cause the board to be recognized as whatever board you had selected from then on. Here's the solution:
Tools > Board > Arduino/Genuino MKR1000
File > New
Sketch > Upload
After that, the board will be recognized as a MKR1000 and your problem with the firmware updater will be solved as well.