Can having marks or different art on the front of cards make any difference to gameplay?
(I'm not looking for Un-set abilities like Art Rampage or cards like "Drawn Together".)
To gain/lose advantage by using different arts would have to involve cards moving between hidden zones. Having different art can only increase information.
It seems this gain of information can work in either yours, or your opponents favour. (As my examples show) But the information gain is minimal. I also suspect it's more likely for your opponent to gain additional info, than for you to. This is because it must involve cards moving between two hidden/private zones (or face-down in a public zone) and there are two zones hidden from your opponent (hand and library), and only one hidden from you (library).
Different arts can be a disadvantage
Your opponent Thoughtseizes you, seeing a Forest with art A, among other cards. Next turn you draw another Forest, art B. Then you destroy your opponent's Black Cat, so you discard a card at random, which happens to be Forest B.
An observant opponent still knows your entire hand, however, had you used the same art, they would not know your most recent draw.
Different arts can be an advantage
Your Triumph of Saint Katherine dies, shuffling it with the top six cards of your library. As you draw your next six cards, there is just one Saint Katherine, but this time in foil.
You now know that the top card is your first Saint Katherine. If they were the same, you wouldn't know.
There is the marginal disadvantage that cards with different arts may leak information about the number of copies of that card that your deck contains. E.g., if your opponent sees one art in game one, and a different art in game two, then they know that your deck contains at least two copies of the card, when otherwise they wouldn't know that.
This is an extremely minor disadvantage and not worth worrying about in most circumstances, but if you're trying to absolutely maximize your advantage in a competitive setting then all else being equal you would generally prefer for all of your copies of a given card to be indistinguishable.
Some players in the old days would play the same art of all there basics. If your opponent saw your hand and saw some lands they could then not deduce that one of your later draws was a land if the basic they saw from the discard spell was the same art as the land you drew.
This made the deck slightly easier to play as you could play either land and not have to worry about playing the land in your opening hand first.
Being able to deduce that one of your opponents cards in hand is a land can influence the do-you-think-they-have-it decision.
This is only marginally useful, but in competitive play these types of min-maxing plays give the fine edges that can be the difference between top 8 and finishing the tournament in 10th place.
It can increase the cognitive load on your opponent. Examples of where it might lead your opponent to making a mistake:
You have two tapped islands with the same art, and a third untapped island with different art. Your opponent forgets about the third island and plays their bomb, only for it to be countered.
You play a bomb in the first game of your match. After the game, you sideboard it out for the same bomb, but different art. In the second game, your opponent plays Bitter Ordeal and doesn't notice the bomb in your deck, and so exiles a different card.
Hopefully it doesn't have to be said that this is bad sportsmanship.