"The old soldier is not fighting, but sitting and having a rest."

Translation: Az idős katona nem harcol, hanem ül és pihen.

[Viviane882195]

What is the difference between idős and öreg?

[vvsey]

Elderly and old. "Idős" is nicer to say.
Also, "idős" is almost exclusively used for people. "Öreg" can be used for other things, as well - probably for personalized objects and things.
There is one more word: "régi". It means "old", in the sense of "from old times". A typical example for that meaning is "an old friend of mine" - someone who can be young but be my friend since childhood.

[Orsi920]

"Öreg" is more commonly used and it is not insulting in my opinion. Like "Öreg néne őzikéje" in literature. :)

[GyrgyFnyes1]

Aki volt katona az nem mond idős katonát, csak öreget. És itt magyarul tanulunk!