This is a closer pic of the skinny/upright plant

just wait till they make berries, which should happen this year

Yeah, they fruited last year so they should fruit again but I want to do some light pruning before then. From what I've read, white and black currants have different growing habits and pruning needs. Blacks fruit on shoots grown the previous summer (and some 2 yr wood) and grow from base of plant (and some 2 yr wood). Whites fruit at the base of one year laterals.

It's hard to tell from the pictures but I'd say the top one is the white and the bottom the black. If you crush the foliage of the second one it should have a pronounced tom cat smell. If you could show close ups, in focus, of twigs and buts I could tell you more definitely.

I can't get very good close-ups but hopefully they'll appear better than the last two.

This is the top one again.

And the latter one.

Yes - the second is the black. When you pick white/pink/red currants the whole strig is gathered. Blacks come off their strigs and they are left behind. You can see them in the second photo. A tip for pruning blacks. You can cut out an entire fruiting branch when harvesting. Take it to comfortable spot and sit down to remove the fruit. Pruned and harvested in one process.