Can anyone tell what plum this is?

Hello all.

We have a Victoria plum tree in our garden. Fine. Behind it is another tree which has done nothing in the last 2 years (since we moved in) but this year it had blossom which looked exactly like the Victoria and now has little fruitlets.

It's been overshadowed for a long time, until we took out the ancient old Bramley last year (shame  ) and has long, long, spiky branches going straight up.

2 questions:

(1) Can you tell us if it is we are right in thinking that this is a plum, and if you have any idea what kind of plum might have this habit?

(2) Can we prune it? I believe now is about the right time for the Victoria (along with thinning its fruit - it's a biennial bearer and we need to teach it  ) but I'm not sure about this one.

Many thanks!