What is the difference between a nice person who is not a christian who helps people out Vs. a Christian who helps people out. I struggle with this thinking. Can we (Christians) do nice things for people with out mentioning a single thing about Christ?
The difference, as I see it, would be that out of an unbeliever's perspective, doing "good" things is entirely optional. There is no objective standard of morality that necessitates doing good towards others, only subjective human opinion. Whereas a Christian is compelled by the objective law of God to do good to ALL people - enemies included, whereas unbelievers for the most part would far rather have their enemies punished.
Out of a Christian perspective, we also have a far better idea of what "good" means, since the teachings of Christ reveal this to us.
Unbelievers can be likened to an uninformed person preparing a gigantic feast for someone who has not eaten in months. Through "good" intentions they can do great harm. They will focus more on the physical, temporal well-being of others, whereas Christians would be more geared towards eventually touching on the deeper issues i.e. purpose in life, finding forgiveness, love, fulfilment etc.
Unbelievers can do amazingly good deeds to help others out, however, it is debatable whether or not they would do so in the way that Christians do. Christians do their good deeds in secret, not wanting to receive special attention or recognition (Christ commanded this way of doing good) What motivation would unbelievers have to behave the same way?
Furthermore, Christians do good towards humans not because they think humanity deserves it - they know it doesn't. We do good towards others despite knowing that they do not deserve it.
Unbelievers think that humanity is good, therefore they treat it with compassion.
In this case, the Christian demonstrates unconditional love and the unbeliever conditional love.
The unbelievers' love is based on the perceived "goodness" of humanity. The Christian's love is present despite the belief of man's fallibility and inherent evil.
To touch on the final issue, yes, it is most certainly possible to do good towards others without mentioning Christ. Introducing people to Him would be the ideal thing to do, though.