There is a chance that there was residual weedkiller in the sprayer. If you sprayed your climber first then the weedkiller left in the sprayer pipe would of come out first, then when you reach your shrub rose, the weedkiller would of been cleared out. The darkening looks just like older rose stem and doesn't look damaged and if it were weedkiller, it wouldn't of affected the bark/stem as quickly as it did the foliage.

Or It may of just been 'got' by a late frost. It should recover once they have gone and the weather warms. You could feed it later in the month to give it a bost, and then cut out and dead shoots if there are any. Maybe it isn't as far advanced as the climbing rose and therefore a little less suseptable to frost.
3 weeks for weedkiller is a little longer though than i would expect weedkiller to start work, but if it were a in the pipe and had been weakened by the black spot spray, the results may of been delayed. 100% esp. one for paths would show signs in hours not weeks.

It's probably to late to hose your rose down as this it what could of been done if you relaised it was weedkiiler say half an hour after spraying, but only if the weather allowed.

Next time, wash and rinse the sprayer 3 times. Washed out, then refilled and clean water pumped through the hose, then washed and rinsed again. Or just ask what your friend uses it for and recommened that they or yourself get a dedicated one for pesticides/fungicides and one for weedkiller, both clearly labelled!

Or, could you have sprayed and then the sun shone on the plant - because that could result in that kind of effect.
The one that wasn't affected might not have been in the sun and therefore not as effected.

Thank-you both. I sprayed them very late afternoon on13th march. Im wondering if nicky is right and there was a frost or bitter wind that night. When I look closely, the generous gardener rose to the side of the pergola is fine, except for the very top branches at the same height as the climbing rose on the pergola, so could it be cold damage to wet leaves? I'm not sure about the weedkiller as the whole rose is affected, and it covers a large pergola so I am thinking that any weedkiller would be washed out on the first stems I sprayed, not the entire large plant.