I tend to agree with Milandro, and I think his definition is a good one.
Back in the day, there really were not these titles or 'levels' of horn, to be associated with how advanced the player was. There were top-shelf, second shelf (aka 'band'), and occasionally super-duper deeeeluxe sorta models.
The monikers of 'student', 'intermediate' did not begin to appear until the late 60's, really. Today, they are the detritus of marketing schemes more than anything else (i.e. the idea that a certain 'level' of horn is the perfect fit for a certain 'level' of player; or that anyone's 'pro' horn will obviously be superior to another's 'intermediate' or even 'student' model).
You see, you said your kid is playing an old Aristocrat. Well...depending on how old.....that may be a Professional-calibre horn. I'd be curious to know the serial number of that sax; understanding of course that it is your sister's. But my point being if you move from certain Aristos to, say, a contemporary 'intermediate'-marketed model, it may likely be a large step DOWN.
Where I disagree with Milandro is where he says that generally the expensive horns are Pro models, the less expensive intermediate or beginner. In fairness to my friend, he then includes some caveats. But I just wanna make sure what he says isn't misunderstood: do not make the assumption that a more expen$ive 'pro' model of one maker is going to be a superior horn to a cheaper intermediate model of another. In some instances, yes. In many instances (particularly dealing with new horns today, 95% of which are asian-produced)...no. A cheaper horn is not necessarily/automatically an inferior one....whether talking new or vintage.
Last comment of my unintentionally long-winded reply:
Rather than get into a can of worms on the Pro vs. Intermediate vs. Student discussion....you would be better off focusing on the crux of your question: getting a good, appropriate sax for your daughter.
In order for folks here to make apt suggestions on THAT, we'd need to know some more info.
She is 12, and has been playing in school for a couple of years.
~ Does she take weekly lessons from a private teacher ?
~ What band(s) is she in, or will she be in ? Is it school concert band, orchestra, stage (Jazz) band, marching band ?
~ Where are you located, and what is your realistic budget for buying her a sax ?
~ Would you consider a second hand horn, or must it be brand-new ?