Spouse’s alias…what is it
On many German birth and marriage records there is a line for spouse’s/mother’s alias. In the cases where is is a mother’s record, this appears to be her maiden name, but on a marriage record, the entry differs from her father’s name. Does this entry refer to her mother’s maiden name or something else.
It's That Dratted Handwriting, but your last example is definitely a widow: "Metta Catharine Reyelt, born Fick, of the late Johann Hinrich Reyelt, something something, widow." In other words, Reyelt is her previous married name, and Fick is her birth name.
Arp??s is clearly labeled as a birth name: 1. 1st Jan. Andreas Tiedemann, something at something and Christine born Arp??s, something son, born something something called Claus. (Followed by a long list of godparents, including the first one with the same surname as Christine, but I still can't read it.)
The marriage record is, um, being difficult, but I think I see: "... and Christine Rüsch, the late ?? Hinrich Rüsch, something something remaining widow." In other words, Rüsch is her previous married name, and the index is wrong about her relationship to Mr. Rüsch.
It looks like the "alias" indexing field is most often used for the woman's birth name (labeled in the actual records as "geboren" or some abbreviation thereof), but you should always check the record itself if possible. If you can't read it, ask in the Germany Genealogy Research group; there are multiple people who hang out there who can actually miraculously read this stuff.1
Without seeing an example, my guess is a previous married name.0
Here are examples
https://familysearch.org/ark:/61903/1:1:QPXB-993V In this case her alias is given as Arpffs, but on this record her father’s name is given as Rusch:
https://familysearch.org/ark:/61903/1:1:QPXB-47DY In this case her father’s name is Reyelt but her alias is Fick.0
Thank you, that is most helpful0