Might be clearer in person, but they're very distinct to an English speaker's ear.

'V' is closer to 'F', while 'W' is closer to 'U'.

It's easier to notice if you exaggerate it. A word starting with V always has the bottom lip touching the top teeth. A word with W has the bottom lip pushed as far forward as possible and never touches teeth.

Just pushing the bottom lip around you can hear the difference from Wine <-> Vine

Dang, was hoping there was a similar enough sound in your native language to help. It appears from my search that there really just isn't anything similar to English W.

Here's my best attempt:

The sound in Turkish represented by U, if you make that sound with a slight vibration at the beginning, you'd get something like "woo" in English. The beginning part of that is the W sound.

With V, the sound you said you couldn't really distinguish from W, the tooth touch the lip in the same position as F, but you vibrate slightly to the V. The W sound isn't really made that way at all, and the sound itself isn't really similar. It looks like two Vs for historical reasons, but in English it represents an entirely different sound.

That's probably a terrible description, but I suck at explaining things. Lol. I do know that when learning another language there are some sounds that you just cannot pick up on if you didn't learn it as a child. I'm not sure if this is one of those, or if you can train yourself to hear it.