Sometimes, but not always.

Standard EXIF usually won’t uniquely identify one unit from another of the same model. Some cameras or phones may store a serial number or unique ID in manufacturer-specific EXIF “maker notes,” but this is not standardized and may not be present.

If metadata doesn’t contain a unique identifier, the next step is image forensics. Individual sensors have tiny manufacturing differences that create a repeatable pattern (often called sensor pattern noise or photo-response non-uniformity). With enough known sample images from each device, a forensic analyst can often match an unknown image to the correct camera, even from JPEGs, though it depends on image quality and compression.

In practice, attribution is usually probabilistic rather than absolute. Metadata, timestamps, GPS, software version, compression behavior, and sensor/lens characteristics can all contribute evidence. So: EXIF alone often won’t prove it, but forensic analysis of the image itself may allow a reliable match between two otherwise identical devices.