It is a fact that much of the teachings that Allah sent Jesus (peace be upon him) with have been lost or corrupted. Thus each Christian is left working out for themselves what constitutes a fast, how to do it etc, and there is no common consensus. Surely Allah alone knows the intention that each individual has, but once the true message has reached someone many times over, in different ways and by different people, over a number of years, then even if one says that they do it to joyfully please God, works without the true faith which God makes clear, will be of no benefit in the hereafter.
But Allah, the Most Merciful, didn't leave them to continue wondering. He sent His final messenger with the final scripture, confirming the truth of what was in the earlier scriptures, preserved til the last days. It may be that some choose to reject this messenger and the message, having understood it, or some may say that they accept the message and the messenger, yet they are not prepared to give up their ways of error as made clear in the message and by the messenger. All of these have a consequence in the hereafter.
People should be under no misperception that they can commit themselves to God as their Lord, and then combine this with accepting others as their Lord, or associating others in His Divinity, or deeming certain humans to be incarnations of Him.
And outside the camp of all the Prophets before Jesus, the Prophet after Jesus, and outside the camp of Jesus himself.
All the Prophets came to tell people to worship Allah alone with no associates whatsoever in His divinity, yet Jesus stands accused of telling people that he was divine, that he was God incarnate, and that people should worship him, which is the opposite of the message Allah sent all the Prophets with and that all the Prophets including Jesus taught. No Prophet before Jesus, nor after Jesus taught that any man was God incarnate or that God begot a son, and neither did Jesus himself:
It is not (possible) for any human being unto whom Allah had given the Scripture and wisdom and the prophethood that he should afterwards have said unto mankind: Be worshippers of me apart from Allah; but (what he said was): Be ye faithful servants of the Lord by virtue of your constant teaching of the Scripture and of your constant study thereof. (Qur'an 3:79)
And [beware the Day] when Allah will say, "O Jesus, Son of Mary, did you say to the people, 'Take me and my mother as deities besides Allah ?'" He will say, "Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen. I said not to them except what You commanded me - to worship Allah , my Lord and your Lord..." (5:116-117, part)
Islam is what all the Prophets preached, it isn't something new, which is a common misconception among non-Muslims, but it is what always was, and has always been, the true and natural religion ordained by God; the way of all the Prophets, the original message, the only message, which Jesus also brought :
He has ordained for you that religion which He enjoined upon Noah and that which We have revealed to you, [O Muhammad], and what We enjoined upon Abraham and Moses and Jesus - to establish the religion and not be divided therein. Difficult for those who associate others with Allah is that to which you invite them. Allah chooses for Himself whom He wills and guides to Himself whoever turns back [to Him]. (42:13)
It clearly states that Muhammad (peace be upon him) is not the founder of any new religion, nor was any of the Prophets a founder of a separate religion, but it has been one and the same religion which all the Prophets have been presenting from Allah from the very beginning, and the same is being presented by Muhammad (peace be upon him).
Nothing is said to you, [O Muhammad], except what was already said to the messengers before you... (41:43)
And when Jesus brought clear proofs, he said, "I have come to you with wisdom and to make clear to you some of that over which you differ, so fear Allah and obey me.
Indeed, Allah is my Lord and your Lord, so worship Him. This is a straight path."
But the denominations from among them differed [and separated], so woe to those who have wronged from the punishment of a painful Day. (43:63-65)
Regardless of what the Christians might have said or done, Jesus (peace be upon him) did not lay claim to being God or the son of God, nor did he ask anyone to worship him. On the contrary, he called people exactly to what the previous Prophets had called and to which the Prophet Muhammad (peace be upon him) was calling, namely, to exclusively serve and worship the one true God.
People went to extremes both in supporting and opposing Jesus (peace be upon him). Those who opposed him went so far as to reject him and blaspheme him, branding him illegitimate. At the other end of the spectrum were those who exaggerated Jesus's status and exalted him to the point of deifying him. But then the question of how a human being could also be God became extremely complicated, with many attempts and efforts to explain it, all of which were unsatisfactory. A number of schisms and sects arose. Muslims believe in Jesus as he was, no more and no less, one the mightiest messengers of God, a sign for all the world, and one of the noblest people to ever walk the face of the earth. I invite you to join us.
Muslims fast to fulfil one of the five pillars of Islam, to follow the way of the previous prophets, to obey God, to seek His pleasure, amongst some of the reasons, and it is a bonus from our Generous, Merciful Lord that there is reward in it for us too.
Some non-Muslims will just see Ramadan as a compulsory fast, which either willingly or unwillingly, you have to do and there is no choice.
Ramadan is completely extraordinary, and fasting during it being compulsory or not doesn't make any difference to the joy and the hope that Muslims feels during this blessed month, the world over.
To Muslims, when it arrives, it's like a most beloved guest with you for a month. When Ramadan finishes, there is utter sadness, that the blessed month has departed, and emotional prayers are said, asking Allah to give us it's reward and to make us alive to see and take part and benefit from the next Ramadan.
Ramadan is the compulsory and well-known period of fasting that everybody knows about, however there are many optional recommended fasts on certain days, eg the six days after Eid al Fitr, Mondays and Thursdays every week, 13th-15th of every lunar month, the day of Arafah, (the day before Eid al Adha), the day Prophet Moses (peace be upon him) was saved etc.
On top of this, we fast on other days of our choosing if we want to, feel the need to, or simply wish to for Allah's sake, and many people do. These fasts are invariably kept quiet, the knowledge of it being between you and Allah alone.
So we get the best of both compulsory and optional, public and private, together and alone, as well as following in the footsteps of the earlier prophets (peace be upon them).