Even the same exact camera will not demonstrate the same "exact" noise characteristics on successive shots. But techniques such as "dark frame subtraction" or other noise reduction processes that measure unexposed areas of the sensor and other characteristics of the noise generated by the camera's circuitry will be "close enough for government work."
Image noise caused by the random nature of light itself, which is often called "shot" noise or "Poisson distribution noise" after French mathematician Siméon Denis Poisson, who developed a discrete probability model that mathematically expresses the phenomenon observed in nature, will vary from frame to frame. How much it will affect an image will depend upon the strength of the light falling upon the sensor, how long that light is allowed to fall on the sensor, and the size and quantum efficiency of the sensor's discrete photodetectors a/k/a pixel wells, photosites, or sensels.
The characteristics of the light obviously will not be the same for disparate images, even when taken with the same camera. But the size and sensitivity of the sensels will be common to a given model line, within the limits of manufacturing tolerances that are fairly high (very little deviation) for the manufacturing of silicon based circuitry.
Cameras with the same manufacturing specifications will also be very similar with regards to the noise generated by the camera's sensor and other electronics when placed in the same environmental conditions. This is often referred to as "read noise" when originating on the sensor and "dark current noise" when originating from elsewhere in the camera's electronics.
Image noise that varies with things such as ambient temperature will also obviously also not be the same in different environmental conditions. The difference between shooting in 0°C (32°F) and shooting in 40°C (104°F) weather with the same exact camera will be much greater than the difference between two copies of the same model when both are in the same environmental conditions.
So the factors that are dependent upon the camera itself will be very, very similar in different samples of the same camera model. That's about the best a "generic" model can do without taking into account things such as the temperatures of the various parts of the camera's sensor and electronics at the time a particular image was taken as well as the differences due to the light falling on the sensor.
