As Dave says, the term "Premium Rate Services" (PRS) has some formal status as it is declared in the Communications Act 2003 with reference to the services delivered on number ranges designated by Ofcom to fall within the self-regulation of PhonePay Plus.
Calls to 0844 and 0845 numbers are subject to revenue sharing and attract a premium charge in effectively the same manner as those to PRS, however they are not designated as being used for PRS.
Other terms have no such formal and general definition over which to have an argument.
"national rate" has been used by BT to describe the rate applicable to calling geographic numbers not designated as "local" to a particular caller. At one time this did apply to calls to 0870 numbers, but never 0844. At this time "local rate" applied to calls to 0845 numbers. The distinction between "national" and "local" rate disappeared in 2004. Ofcom has introduced the term "UK rate" to apply to that applicable to calls to geographic numbers.
Some providers use the wholly misleading term "lo-call" with reference to calls to 0844 and 0845 numbers. This reflects the fact that the premium charged on these calls is "lo"wer than that on calls to PRS numbers. The term is however used to imply that the cost is low in absolute rather than relative terms.
In the absence of any regulation covering the charge made for calling 0844 and 0845 numbers (except those applicable to BT because of its unique status), or of the manner in which the charge is declared by users of the numbers, one may describe it in any way that does not fall foul of the restrictions imposed by Trading Standards or the ASA. I personally describe the charge as being a premium rate, although always without placing this in parentheses, as it is not a formally defined term. It reflects the simple reality that the rate charged includes a premium element.
(Perhaps someone better versed in such matters would like to collate and polish these comments and
update the relevant Wikipedia entry for the UK.)
My advice to Biscuity is to put aside semantic argument so as to get the true point across. The user of the 0844 number benefits from the revenue sharing process at the expense of callers (unless the Telco is being allowed to rip-off both parties). If they are content with that, then they owe callers an explanation of why their service by telephone warrants a charge. If unaware of this, perhaps having been misled by their provider, they should be invited to verify the truth of the situation and then come back with a comment about what they are going to do about it.