Zaid in verse 33:37.

[Sleepysoul]

Salamun'Alaykum,

I have a question. I don't quite understand the verse about Zaid. Some say he's the adopted son of the Prophet himself (secondary sources confirm this), I saw a translation which suggests that Zaid is just a name used in Arabic to describe any Tom, Dick and Harry, yet I also saw the following translation which does not even mention the name Zaid:

"And (remember) when (he) said to him  “you have received the grace of Allah and  favour: "Retain thou (in wedlock) thy wife, and fear Allah." But didst hide in the heart that which Allah was about to make manifest: and didst fear the people, but Allah had better right that he should have feared Him. So when their desire to finally end the union increased We joined her in a new marriage tie: in order that (in future) there may be no difficulty to the Believers in the wives  yearning/cry, when the latter have dissolved with the necessary (formality) (their marriage) with them. And Allah's command must be fulfilled."

More common rendering:

"And [remember, O Muhammad], when you said to the one on whom Allah bestowed favor and you bestowed favor, "Keep your wife and fear Allah ," while you concealed within yourself that which Allah is to disclose. And you feared the people, while Allah has more right that you fear Him. So when Zayd had no longer any need for her, We married her to you in order that there not be upon the believers any discomfort concerning the wives of their adopted sons when they no longer have need of them. And ever is the command of Allah accomplished." - Sahih International.

In the verse, the Prophet says "Keep your wife and fear Allah". What does this mean? Was Zaid divorcing and offering his wife to the Prophet? Or did the Prophet want to marry her? Was the Prophet merely worried of the thought of divorce? If yes, then the first translation makes sense. If the whole idea was to marry the Prophet to Zaid's wife to show that one can marry wives of adopted sons then why would the Prophet tell Zaid to keep his wife unless it meant that he couldn't marry her due to society? This seems confusing to me.
Then we also have a verse which tells the Prophet that he's not allowed to take any more wives. I'm assuming that was after this if we use the second translation.

Thanks for your answers.