Military (?) buttons / lapel pins - Need help id'ing - WWI or WWII era

[Wavydavy67]

I could use some help identifying these. I found them in a small box, and I think they belonged to either my father, who served in WWII, or my grandfather, who served in WWI. Any ideas what these are and from what time period? Thanks!

 

[jadocs]

It's not military. I've never seen anything like it.

Edit: I should say it's not US military.

 

[nhbenz]

I don't offhand recognize it either, but it may help in the search to know the size, fastener type, and any marks on the back.

 

[Wavydavy67]

More detail

They are about ⅜" across, but the back part is slightly larger (about 7/16"). The backs do not appear to be removable. I'm attaching images of the cross section. There are no markings of any kid on the backs, and the posts attaching the front and back are slightly different construction, which indicates to me that they were not made at the same time (i.e. a set of cuff links). The red color is also slightly darker on one, as are the stars.

 

[NOLA_Ken]

I wonder if they are old time collar studs?

https://en.wikipedia.org/wiki/Detachable_collar

 

[Keith Jackson]

I wonder if they are old time collar studs?

https://en.wikipedia.org/wiki/Detachable_collar

That definitely seems reasonable if the ones posted truly are 2 separate items and not a pair.