Photo/iPhoto differences, images disappearing - help!

After updating to 10.10.5, Photos is not performing as it once did, but I haven't been able to find the answer to make it work, despite much searching.
After highlighting several photos in Photostream, creating a New Album and naming it, I would then delete the photos from Photostream.
Now, with the 'upgrade' to Photos, if I do that, my pics disappear from the album.
I had to go to 'Show Recently Deleted' in Photos to get the images back.
Can anyone explain what has changed and how Photos works differently from iPhoto?
TIA

Nothing has changed, as far as I can determine.

It appears that what has changed on your end is that Photostream is where those photos are filed/exist. Albums are (and always have been) subsets of the pictures from the main library. If one deletes the photos from the library where those pictures "live" -- they will of course be removed from any subset (albums, smart albums, projects, etc). This is not new.

If I'm correct that the photos only exist on "Photostream," that could be an indication that you have turned on iCloud Photo Library (perhaps -- don't know enough about IPL yet) or that you made a change in preferences. First thing to do is check there. If iCloud Photo Library is turned on, what happens if you try turning it off?

"Albums are (and always have been) subsets of the pictures from the main library. If one deletes the photos from the library where those pictures "live" -- they will of course be removed from any subset (albums, smart albums, projects, etc). This is not new."

True. I knew that. What is new: If I delete a photo from Photostream in Photos on the computer, AFTER creating a new album for the pic, it disappears from the album. It never did before. (this is how I cleared Photostream previously: Create a new album for photos, then delete them from Photostream on the computer)
Now:
- Select pics for a new album
- Delete photos from Photostream on iPhone only (not on computer)
- Photos remain in the album

RE: iCloud library - it is not turned on. No change made in preferences.
I still can't figure out why, when trying to post a photo to fb, the most recent pics don't show up in Photos. That remains a mystery.