Prophethood is not to Continue in the Same Fashion as was During the Judaic Dispensation

Some hadith (tradition of the Prophet) may indicate, that the sealing of the office of prophethood, is to be understood in the light of the manner of, how guidance was continued in previous dispensations, and how that method was changed in Islam.
Through Muhammad's revelation the office of prophethood was ended. That is to say, no other prophet like those of Judaism (like Isaiah, Jeremiah, Daniel, Ezekiel, Zechariah, etc... ) were to appear. Instead Khalifs (according to Sunni terminology), and Imams (according to Shi'ite usage) appeared. The following Sahih Hadith hints at this issue:

Narrated Abu Huraira: The Prophet said, "The Israelis used to be ruled and guided by prophets: Whenever a prophet died, another would take over his place. There will be no prophet after me, but there will be Caliphs who will increase in number."
The people asked, "O Allah's Apostle! What do you order us (to do)?" He said, "Obey the one who will be given the pledge of allegiance first. Fulfill their (i.e. the Caliphs) rights, for Allah will ask them about (any shortcoming) in ruling those Allah has put under their guardianship." - Sahih Bukhari 4:661 (see Arabic)

The Prophet (PBUH), had adopted Zaid ibn Al-Haritha and treated him as His own son and made him part of His household. The people started calling him Zaid ibn Muhammad. Verses 4 and 5 of the same sura, clearly discourage such practice :

[33:4]
YUSUFALI: Allah has not made for any man two hearts in his (one) body: nor has He made your wives whom ye divorce by Zihar your mothers: nor has He made your adopted sons your sons. Such is (only) your (manner of) speech by your mouths. But Allah tells (you) the Truth, and He shows the (right) Way.
PICKTHAL: Allah hath not assigned unto any man two hearts within his body, nor hath He made your wives whom ye declare (to be your mothers) your mothers, nor hath He made those whom ye claim (to be your sons) your sons. This is but a saying of your mouths. But Allah saith the truth and He showeth the way.
SHAKIR: Allah has not made for any man two hearts within him; nor has He made your wives whose backs you liken to the backs of your mothers as your mothers, nor has He made those whom you assert to be your sons your real sons; these are the words of your mouths; and Allah speaks the truth and He guides to the way.

[33:5]
YUSUFALI: Call them by (the names of) their fathers: that is juster in the sight of Allah. But if ye know not their father's (names, call them) your Brothers in faith, or your maulas. But there is no blame on you if ye make a mistake therein: (what counts is) the intention of your hearts: and Allah is Oft-Returning, Most Merciful.
PICKTHAL: Proclaim their real parentage. That will be more equitable in the sight of Allah. And if ye know not their fathers, then (they are) your brethren in the faith, and your clients. And there is no sin for you in the mistakes that ye make unintentionally, but what your hearts purpose (that will be a sin for you). Allah is ever Forgiving, Merciful.
SHAKIR: Assert their relationship to their fathers; this is more equitable with Allah; but if you do not know their fathers, then they are your brethren in faith and your friends; and there is no blame on you concerning that in which you made a mistake, but (concerning) that which your hearts do purposely (blame may rest on you), and Allah is Forgiving, Merciful.

As people were using the name Zaid ibn Muhammad, the expectation of some was also that he would become His successor, as had been the case the prophets of the children of Israel.

When Zaid divorced his wife, who later was married to the Prophet (PBUH), many people objected to this and expressed their displeasure that He would marry His "son's" divorced wife, verse 33:40 made it clear that Zaid was neither the Prophet's son nor was he or anyone else to be a prophet after Him.

When chapter 33 is read in its entirety, this issue becomes much clearer.