The 5-pt harness matters, a LOT. In the US, it is the crux of the whole issue.
You see, when an airline says that a "booster seat" cannot be used on an aircraft, the airline is making reference to what the FAA defines as a booster seat. In the context of US air travel, it does not matter what the mfr. of the seat chooses to call that seat. What counts is whether or not it has an integrated shoulder harness attached.
Under the FAA definition, a "booster seat" is a carseat that lacks integral upper-body restraints. Therefore, if your carseat has integral upper-body restraints attached and in use, it is NOT a booster seat as defined by the FAA.
Check the frame of your carseat for an FAA aircraft approval label. If it has one (and it should, if it was mfr'd after 1985) it can be used for aircraft travel if you comply with the conditions specified on the label. For a seat with a removable harness, that label usually specifies that the seat is only approved for use on aircraft if the 5-pt. harness is used to restrain the child.
References: US Code of Federal Regulations, 14CFR135.28 and 49CFR571.213. You can read the definitions for yourself by going to
http://www.gpoaccess.gov/cfr/retrieve.html and plugging in the citations.