The history is dissimilar, but what they both stood for is very much in sync. The only difference is the source and the practices themselves. Christ got His words from His Father. Buddha got His Words from observing Himself and the world around Him which lead to His enlightenment.
They are similar in that:
Christ told us to follow His Father by celebrating His Life, Death, and Resurrection with communion with others.
The Buddha said "As long as the followers of the Way hold regular and frequent assemblies, they may be expected to prosper and not decline. As long as they meet in harmony, break up in harmony, and carry on in their business in harmony, they may be expected to prosper and not decline. (Mahapartnibbanna Sutta)
Both said they we have a holy nature within us. Christ said that everyone is pulled by God (so no one person is alone and just all of the sudden say "I want to believe") and He said that those His Father Has chosen
as well as those who are willing to say yes, have the Holy Spirit within them--new nature.
The Buddha said that we all have a Buddha Nature (Mahayana) to which we are always aware of when we are not attached to things that Christ and The Buddha said were sins such as greed, killing, lust, and so have you.
"There is no fire like greed, no crime like hatred, no sorrow like separation, no sickness like hunger of the heart, and no joy like the joy of freedom. Health, contentment, and trust are your greatest possessions and freedom your greatest joy. Look within, be still, free from fear and attachment, know the sweet joy of living in the Way." (Dhammapada)
What separates the two is is Christ said look to His Father. The Buddha said look to yourself.
Other than that, Christianity is an eastern religion (eastern origins), so I wouldn't be surprised if someone eastern concepts mixed in Christian faith. The Buddha was alive long before the Church came to be.
The Buddha's teachings are eternal. "Since I attained Buddhahood the number of kalpas that have passed is immeasurable...constantly I have preached the Law to convert millions of living beings to enter the Buddha Way. [You-His disciples--think] I appear to enter nirvana but in truth I do not pass into extinction. I am always here, preaching the Law." (LS pg 21)