Many languages distinguish between inclusive and exclusive first-person plural pronouns (“we”). (Click or tap here to see more details)
The inclusive “we” specifically includes the addressee (“you and I and possibly others”), while the exclusive “we” specifically excludes the addressee (“he/she/they and I, but not you”). This grammatical distinction is called “clusivity.” While Semitic languages such as Hebrew or most Indo-European languages such as Greek or English do not make that distinction, translators of languages with that distinction have to make a choice every time they encounter “we” or a form thereof (in English: “we,” “our,” or “us”).
For this verse, translators typically select the exclusive form for the first occurrence (“we write” in English) (excluding the reader) and the inclusive or the exclusive form for the second (“our joy” in English). Note that some manuscripts and therefore some translations have “your joy” instead.
Source: SIL International Translation Department (1999).