Thats one way to put it
Sweeper even said so himself, the is one past, one future, but two presents.
Sort of but only until Old Sam goes back to his proper timeline - from that point the present becomes the one where Keel died and Future Sam took his place - but young Sam who went on to grow into Old Sam pre-timeloop
never knew any different until he gets back. Same thing for Vetinari when he encounters Sam at the Small Gods cemetary - the Keel he knew when he was young was always Keel so far as he was concerned until he found out.
It's just a perception of the present and young Sam isn't fundamentally altered because he only ever knew 'Keel' as Keel so his history isn't really altered in any meaningful way. Old Sam is still the sum of his experience so his own memory of Keel as Keel is still intact and of course made him the man he is in the present, in part because Keel was his ideal and hero - that all still gets tarnished once history is re-established. In fact you could argue that without either Keel to idolise, Sam would never have become so disillusioned with the Watch and it's degradation under the Patrician(s) who come in after that first Lilac day and why he ended up a drunk in love with a City that only existed in his memory of what might have been.