The second type refers to the present,
• If I WERE* a billionaire, I WOULD buy a castle.
• Even if I KNEW her name, I WOULD not tell you.
СONDITIONAL 2 (PRESENT)
If+Past ✕ Would
All of these sentences are about an alternative present. "If wishes were horses..." and so on.
It's not necessarily purely wishful thinking. A mere "if":
* You aren't seeing things. In conditionals, WERE can be used even with a singular subject.
• If you BEHAVED yourself, I WOULD TAKE you to the zoo now.
• If he WASN'T/WEREN'T Russian, he WOULD need to learn Cyrillic.
Sometimes, it is just a polite request:
• I WOULD be very grateful if you COULD just shut up.
which could possibly be different, but it's not: