Es i = "I went"
Dw i wedi mynd = "I've gone"
Simple past (went) is often used with a word or phrase that indicates when you did something. I went to the office yesterday. Present perfect is usually used without being specific about time. I have gone to the city. It sounds a bit odd in English because if you have gone, you aren't here, so can't be talking to the person, except maybe on the phone or in a note.
This sounds very odd in English: it could be a note left for someone at home who was expecting you to be there; later in the day, when you got back, you would say, "I have been to/at the office"; or, "I went to the office".
Think of it as writing a note, saying that "I have gone out. I have gone to work" - i.e. you're still out (whereas"I went out" would imply that you were out but has come back). I'm not a native English speaker, but English follows Swedish here (making it easier for me to grasp the subtile difference).