Over the recent weeks I have been twice in a skirmish on the correct use of the terms recto and verso, and I blame the dark days of early papyrology for this (there are articles on this topic; I leave it to commentators to share that wisdom). Before the dawn of papyrology everyone knew what the recto and verso of a manuscript page were: the recto is the front, the verso the back, identified on the basis of the direction of the text. On paper the physical aspects of either side of the page are (virtually?) indistinguishable; on parchment there is a hair and flesh side, though with well prepared parchment there is not that much of a striking difference. However, on papyrus there is the writing either along the direction of the strips of papyrus or across these. But still, recto and verso are terms based on the direction of the text, not on any physical aspect of the material.
Then there were papyrologists. And they described rolls, where the primary writing is on the 'along side' (normally the inner side of the roll), and where there is possibly secondary writing on the 'across side' (normally the outer side of the roll). Or other reused sheets of papyrus, where, again, the first text is along, and the secondary text across (normally). And the terms recto and verso were used so that they became often identical with along and across the direction of the fibres.
I think that this explains the odd labelling on the actual frames of P45, where the folio number is followed by a 'r' or 'v' which indicates not the direction of the text, but the direction of the fibres. In the transcription on the INTF website the same terms are used, but there correctly. This results in regular mismatches between the labelling on the frame and on the transcription. E.g. folio 16:
These days papyrologists tend to avoid the terms recto and verso (and rightly so, at least in their world), but within book studies (codicology proper) the terms have a rightful place as describing the direction of the text.
Physical description Parchment: Hair - Flesh. Papyrus: Along (→) - Across (↓)
Text direction (not related to the physical description!) Parchment: Recto - Verso. Papyrus: Recto - Verso (only really useful in papyrus codices)
It is only now with electronic texts and webpages that recto and verso have lost their relevance.