2 Euro Belgium 2004 - with & without circle

is this a rare coin to find?

No

Doesn't look like scratches from a machine. But it is still not that special or interesting to the vast majority of collectors. The center coin part may have been a tiny bit on the large side and excess material got pushed out of bounds or it wasn't set perfectly etc. there are multiple reasons for such unusual metal flow.

It looks to me like scratches from a coin rolling machine too. In my opinion it's clearly to see on the enlarged part of the coin, this is not done during the minting process.

Okay, I enlarged the bottom picture and there it wasn't that obvious and I thought the transition fold between the inner and outer ring was meant. Yes, those lines look more like scratches that go over design elements.