This should explain: https://www.nerdmuch.com/mtg-arena-vs-mtgo/
If you're choosing between the two, I would recommend MTG Arena. Unlike MTGO, there's 3D animation and effects, card styles, and is free (as long as you're not playing competitively).
What is the difference between Magic the Gathering:Online and MTG Arena
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As someone who has used both, my opinion on this would just be that they are for distinctly different things and should not be directly compared. They are both free to download, but have different economy systems and UI/UX's. Arena is completely free to play, and you could theoretically acquire every card for free, but the Arena economy is so stacked against f2p players that that is basically impossible. On arena you can really only play draft, sealed, brawl, standard, and historic. The UI of Arena is overall nice, but has many flaws. On the other hand, MTGO is a platform with an economy modeled after real life. Cards and drafts cost money, but let you build any deck you want for literally any format. The price of cards on MTGO are very different than real life, letting you essentially build a top-tier competitive deck for under $30, or a fun, janky, but still powerful deck for mere cents. The only way to describe the MTGO UI is just plain bad.
Generally, if you want to be able to jump right into any format with any deck, I would recommend MTGO. If you don't want to spend money, or want a nicer UI, MTGA is the way to go. There are many more things to consider, but thats the basic gist of it.
^^