I am a wee bit confused - are the first three all the same and the third one different? Or are these all the same plant?

These are all from the same honeysuckle at different times of the year. The last picture above is from early in the growing season, before that round leaf that ends each branch opens up...

Probably Lonicera caprifolium.

The pictures of caprifolium that I see online show white blooms. Mine are peachy...

Check Google images: flower color is somewhat variable and there seems to be as many photos of this species with peach or pinkish colored flowers as there are those with paler white-yellow flowers.
Lonicera caprifolium with peach colored blooms.

I imagine the reason GG suggested L caprifolium is because of those leaves which encircle the stem. That's a perfoliate arrangement and l caprifolium's common name is perfoliate honeysuckle.

Lonicera tellmanniana also has perfoliate foliage. See if that looks like yours. The colour looks a bit better fit.

I've just read about tellmanniana and that seems to be a better fit. The images are more familiar to my recollection. I find it hard to believe I've never taken a picture of the blooms open, I have to dig around to see if I can find one. This would also explain why I've never smelt it; I thought I wasn't perceptive enough to notice the perfume... The link I consulted said that it is scentless.

Is it a wildling or an intentionally planted vine? That could clarify the issue. L. tellmanniana is a hybrid and would have been intentionally planted. It is also not at all a very common selection of honeysuckle in this country, in fact I know of no nurseries that carry it. OTOH, caprifolium is a borderline invasive species and has naturalized in much of the South.

I'm in Canada, greater Montreal area. The vine was not planted by me, but I'm quite sure it was on purpose. I should go see what varieties are sold locally, presuming that whatever I have is likely to be available there. Somehow, that hadn't occurred to me...

I'm in Canada, greater Montreal area. The vine was not planted by me, but I'm quite sure it was on purpose. I should go see what varieties are sold locally, presuming that whatever I have is likely to be available there. Somehow, that hadn't occurred to me...