Is a spice model unique?
No, they're the furthest thing from being unique unless they're just copied.
In general SPICE models reflect typical characteristics, to some degree of accuracy. Datasheets offer 'typical' characteristics, sometimes, but the min/max is usually what we are most interested in.
A jellybean transistor eg. 2N3904 from manufacturer A may meet all the min/max JEDEC limits, but have different typical characteristics. Maybe they were actually designed as a somewhat better transistor and now they decided to package them as the lower performance part. Processes vary.
Sometimes models are optimized to run quickly at the expense of accuracy, because otherwise it would be difficult to run useful simulations.
Sometimes manufacturers have proprietary tricks that they feel might be compromised by revealing the entire model so they encrypt the model and unencrypted models are macromodels or just not available.
Sometimes the models are just not very good. Maybe a student or volunteer did it and released it to the wild.
Manufacturers have an interest in selling their products, so using a model the manufacturer you are planning on using has on their website is usually a good idea.
For example, as you probably know, the most important DC characteristic of a diode at low-ish currents is the forward saturation current Is in the SPICE model. You will find the number for a common part such as 1N4148 varies by 3:1 or more between different manufacturers. Since there is a ln in there, that's only about a +/-5% variation in Vf so it isn't as bad as it sounds. However you'll find also find it specified as eg. 4.352nA, to a silly number of decimal places, or to just one decimal place (eg. 7nA).
Depending blindly on the 'typical' characteristics, as described in the datasheet or in a SPICE model is a recipe for disaster. Design first then verify with simulation and prototyping. The typical characteristics can be useful in evaluating the limits and in understanding operation in a multi-dimensional space that is only guaranteed at a few points at best, that's why they're there, but one must take care.