Hi! The reason you are puzzled is because the general knowledge among people is that Prophet Muhammad (pbuh) started the religion of Islam.
Well actually as Muslims we believe that God send messengers throughout time since the first man on earth. They all came with the same message of belief in One God. It's obligatory as Muslims to believe in all these prophets / messengers.
Every prophet was sent to a particular group of people.
And therefore while the fundamentals of the message were identical (One God, this life and the next life, angels etc), however the little details of how to pray and fast etc were different depending on the time period each prophet was sent to and also the country or region they were sent to so as to make the message easy for the people there accordingly.
So similarly Jesus and Moses were sent at different times but carrying the same fundamental message.
And so did Muhammad come with the same message carrying on the legacy of all the previous prophets. Peace be upon them all
All of these prophets were from the same God and the same fundamental message of belief in one God. But the details of how to pray differed depending on the time period and group that they were sent in.
We believe as Muslims that the last prophet that was sent was Muhammad. There will be no other prophet sent after him. And therefore his message is for all humanity until the end of time (unlike the previous prophets who were only sent to a group of people for fixed time, not eternity) -- this is important to understand.
Since this is a fundamental tenet of Islam, it's safe to say all these prophets are of the same religion.
And therefore easy to conclude that Jesus is Muslim because Muhammad himself said he is simply carrying forward the message of all the previous prophets.
Peace be upon all the Prophets
(Another thing to note is that the books that were sent by God to Moses, Jesus were meddled with by humans and therefore the Word is not accurate as it was initially sent. However the book that God gave to Muhammad (pbuh) is preserved and God has promised that this book will not be meddled with by humans until the end of time. And therefore you will find that the Quran is exactly the same across all Muslim groups across the world today as it was since the time of the Prophet Muhammad pbuh 1445 years ago)
Hope that clarifies and happy to discuss more.