It was our Tea rose study group that noticed "Vestey's Pink Tea" is the same as 'General Schablikine' while we were researching the roses for the Tea rose book. This wasn't done in haste or based on the comparison of single plants.
The roses were growing side by side in the display garden of Melvilles rose Nursery near Perth in the late 1990s and this is where we first noted that they appeared to be the same.
I have a number of quotations on the pinup board behind my computer that I find useful when researching roses and anything else for that matter. One of them is Richard Buckminster Fuller's "You uncover what is when you get rid of what isn’t." and another, this humbling one by the late Trevor Griffiths "Identification is a complex subject. The worst mistake that can be made is that you should assume the name for your particular rose is the correct one and that everyone else is wrong." (from A Celebration of Old Roses p15).

There is always a lot of that about - between the six who researched and wrote the book, we probably had every misnamed Tea rose in the country growing in our gardens so we were very aware of the perils of mislabeling and the difficulties that can arise when sorting out which (and whose) roses are correctly named. To check for the possibility that Melvilles might have a misnamed rose, we ordered roses from a number of interstate nurseries and, in this case, we always received the same rose under the name "Vestey's Pink Tea". 'General Schablikine' was a different matter - apart from 'General Schablikine labelled 'General Schablikine', some nurseries were sending out 'Mons Tillier' as 'General Schablikine' and some sent 'General Gallieni' (and vice versa). We also received "[not] Souvenir d'Un Ami" with a 'General Schablikine' label.

For our book to be useful, we needed to know whether we (ie, East, Central and West Australian gardeners) were growing the same Tea roses under the same names and, if there were discrepancies, to understand what and where they were, and how they come about. So we took every opportunity to visit collections in nurseries and gardens in other states. Of course there were discrepancies - even with the utmost diligence, there are inevitably occasional errors in labeling and once they get into a distribution stream, the errors spread, sometimes quite widely. The good news was that the discrepancies were where they were expected to be, and thanks to information shared by nursery people and rose collectors, for reasons we came to understand.
Rustons Roses, at that time the main supplier of budwood to Australian rose nurseries, had stock plants of both 'General Schablikine' and "Vestey's Pink Tea" and we had the opportunity to examine them closely on a number of visits to the garden in Renmark. 'General Schablikine', like most Teas, varies in bloom form and colour with the seasons and in response to different conditions and rootstocks but at Rustons Roses, as in Melville's Nursery, the roses were undoubtedly the same. After we drew David Ruston's attention to this he watched his plants like a hawk and after a number of years he told us he was in complete agreement.
We were satisfied the roses were the same before publishing the information.
It is always good to have an analytical eye on rose identification work. Thank you for your careful observations and reasoning. I hope you are able to strike cuttings of both your roses and to eventually grow them in the same conditions and that this discussion can continue in the future. With enough time and patience, the roses do give up their answers.