Why are Jews called Jewish?

I mean, being Jewish is a religion, it's not a nationally, yet when you ask them "What are you?" they just say "I'm Jewish". I was born in Israel, my dad in Russia, my mom in Caucasus. People often mistake me for being Russian even though I'm like 1/8 Russian. I tell them I'm from Israel and they automatically say I'm Jewish. I'm not Jewish, I'm Hebrew/Israeli. So why did being Jewish become a nationally? Normally, people in Israel are either Ashkenazim, Moroccan, Yemeni, Romania, Armenian etc. But in the US they are none of that, they're just 'Jewish'. Also, what's up with the stereotype that 'Jews' have a big nose'? Maybe they're Armenian, or Caucasian...