What Is The Difference Between Translation And Interpreting?

You are correct in saying that translation is generally written, while interpreting is oral. You translate a document, you interpret for someone in a foreign language. They are not interchangeable.
Everyone who is claiming that “interpreting” means “less literal” are using it in a different context. Look at any book that was originally written in a different language, and you will see that someone is listed at “the translator” NOT as “the interpreter.”

Interpreting is the translation of the spoken word, this can include paraphrasing and changing the literal translation to improve the context in the language being translated to add understanding, colloquialism and dialect.
The written word is never “interpreted”, but is always “translated”.

Years ago I worked as a translator in UK (ie I translated the written word) then I worked in Brussels as an interpreter, and I had to sit in a cubicle and interpret four languages at international conferences for 8 hours a day non-stop. It was lucrative work but very hard – people think you are a machine, and not human. You burn out at 30 and go and do something else.
I’m sure things are very different nowadays but then you got put into a cubicle with head phones on and you just switched from one language to another and you had to know all the vocabulary, idioms, etc for all languages.

they’re synonyms.

This is a typical pair of English words–they are virtually identical in meaning and can usually always be interchanged, but native speakers work very hard to find a difference between them.
In terms of working between two languages, the works are identical. Either can be used in either context. Sometimes, one is more common than the other (translation is more common in referring to writing, but both are equally common in referring to spoken language), but both can legitimately used in either context.
The only real difference comes in terms of literature. “I interpreted the works of Dickens” means “I explained the meaning of the works of Dickens,” while “I translated the works of Dickens” usually means “I took the works of Dickens and turned them into Spanish” although it can still mean “I explained the meaning of the works of Dickens to a very stupid audience of English speakers”.
In other words, the two are virtually identical in meaning and there is NO context in which one is correct and the other incorrect. The ONLY difference is how common either one is in either context. It’s not a question of correctness or grammaticality, it’s a question of frequency of usage.

Interpret the way you used it may mean to provide additional meaning to the document, not necessarily to another language. You can translate orally and in writting. You can also interpet orally and in writting.

Interpreting takes into account context and setting. Translation is a word-by-word or phrase-by-phrase conversion. Think Bible.

Translation : The act or process of translating, especially from one language into another.
Interpreting: To explain the meaning of …to translate orally.

they are spelled different

I’d say interpreting is less literal. Trasnlating is to convert as word-for-word as possible, whereas interpreting is an attempt to convery the meaning rather than the words.