Hello there PierreDavid,
It sounds like you are deleting one photo on one device and then it gets removed from all your devices. That indicates to me that you have iCloud Photo Library enabled, and if so that is expected:
When you delete a photo or video from your Photos app, it will also delete from your iCloud Photo Library and iCloud storage. You can recover your photos and videos from the Recently Deleted album for 30 days.
From: Get help with your iCloud Photo Library
You can toggle that option in your Settings if you wish:
- In iOS 8.3 or later, go to Settings > iCloud > Photos, then turn on iCloud Photo Library.
- In OS X 10.10.3 or later, go to System Preferences > iCloud > Options next to Photos, then select iCloud Photo Library.
From: iCloud Photo Library FAQ
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