Well, as for me there isn't much same words with different meaning
for example:
- краватка (UA) = галстук (RU) = tie
- краватка (RU) = ліжко (UA) = small bed
Some words have different gender:
- собака (RU female) = собака (UA male) = dog
There are lots of words with different spelling which has the same meaning:
- карандаш (RU) = олівець (UA) = pencil
I think Ukrainian has more influenced from western languages through its history:
- фортеця (UA) = крепость (RU) = fortress
- файно (UA) = хорошо (RU)= fine
But of course many of Russian and Ukrainian words have the same roots but their derivation, suffix, ending are different.