This page lays out major differences between foil-etched and regular foil cards in Magic: The Gathering.
The new "etched" foiling in Magic comes with some advantages. Its most important advantage is that foil-etched cards won't warp or bend. Below, you can see a foil-etched Prossh, from Commander Legends:
Foil-etched cards appear slightly matte and are a little less shiny on the foiled portions. They have a slightly textured finish compared with regular foils and, as a result, there is less glare reflected off the card. You will notice a metallic granular finish that looks as though it contains tiny metal specks.
Mystical Archive Foil-etched cards are slightly different from other foil-etched cards. Below you will see pictures of both English and Japanese Mystical Archive foil-etched cards:
For Mystical Archive foil-etched cards, only the small gold segments to the left and right of the title and text box are shiny.
Japanese Mystical Archive cards have a subtle shiny frame around the text and the card type box. On these cards, the golden frame around the cards is not shiny and only has a golden sheen on White-color cards.
Foil-etched cards appear as a separate version on Cardmarket. Because they can be harder to identify than regular foils, we decided not to support them as an attribute. For Mystical Archive, you'll notice that there are four versions per card. V1 is the regular English language card; V2 is the regular Japanese language card; V3 is the foil-etched English language card, and V4 is the foil-etched Japanese language card. You can see an example here with Chaos Warp.
For Modern Horizons 2, we also use different versions, like in Mystical Archives, but because of the variations in versions per card, we do not use a consistent numbering scheme to distinguish which versions are foil-etched and which are not. Instead, we recommend looking at the tag on the card image, which you can see in the picture above.
For other sets with foil-etched cards, like Kaldheim or Commander: Legends, you will notice that we have a separate "Extras" set, where we include the foil-etched versions of the cards. This is because there is no "regular" version of the card from these expansions. All foil-etched versions, in these cases, will be included in the "Extras" expansion.