[advanced riders] ride their own horses or have the ability to ride horses that aren't "riding school broke". They not only have secure seats and subtle aids but also are competent in a range of things relevant to their discipline. They can handle a greener horse or one that is unsettled, nervous etc. They may even do basic training but not on a commercial level.
That's, sort of, me. I'm primarily a jumpers rider, and can keep a hot/forward horse under control [I jump my gelding in a pelham but very rarely have to pick up the curb - he is nearly always on the snaffle rein - I just like to have it there just in case], adjust the stride length and rhythm, ride a horse that likes to take the long spot deep into a fence, see my spot, and I'm starting to be able to see my stride far enough out to adjust it if necessary. I can handle double reins easily enough and can jump on whatever release is necessary for the fence and the stride. My auto release needs a little work but my crest release is awesome.
I have a young horse I am in the process of breaking [groundwork until March/April-ish] and often get on a friend's young green TB mare to school her if my friend is struggling.
I ride bareback regularly, and can ride a 180-degree spin and control an attempt to take off without being in any danger of losing my seat. I walk, trot, canter and jump bareback and can ride out my gelding's occasional pigroots and crow hops no problem.
However, I do not consider myself an experienced rider, because I have one big downfall - my DRESSAGE skills, which are vital for any English rider to have, leave a lot to be desired. Sure I can ride a horse walk trot canter and have it round and through from behind [if it's built and trained for it - my gelding is trained but long and thus difficult to keep together], sit the trot for a reasonable length of time, and I know the aids for some basic laterals... but I'm no FEI competitor.
To me, levels are too subjective to really put a label on... as a rule when I'm looking for horses I look for either young and green [because 'experienced rider only' is pretty much a given with a greenie, but I have a pretty good idea of how to train the green horse for the basics of most any English discipline so if it's only its greenness that makes it unsuitable for a novice I'm ok] or something that is advertised as suitable for an intermediate level rider. I like starting my own because any problems are then my fault and I cannot blame anyone else! I am forced to look seriously at myself, instead, because if it's the "horse's" fault, it's the person who trained it's fault... ie me.