"Agnostic" in normal usage today means "don't know" or having an open mind about religious belief, especially the existence of God. It can also mean something much firmer: that nothing is known, or can possibly be known, about God or supernatural phenomena, and that it is wrong to claim otherwise. That is the original meaning of the word, and 19th century "agnostics" lived their lives atheistically in practice - that is, without any reference to any concepts of gods or the supernatural.
"Atheist" includes those who reject a belief in the existence of God or gods and those who simply choose to live without God or gods. Along with this will usually go disbelief in
the soul, an afterlife, and all other religious beliefs.
"Freethinker" is used of those who reject authority and tradition in matters of all belief, including religious belief, preferring to think for themselves. It was a very popular term in the 19th century and is still used in some European countries by non-religious organisations to describe himself.
"Humanist" is used today to mean those who seek to live good lives without religious or superstitious beliefs. A humanist may embrace all or most of the other approaches introduced here, and in addition humanists believe that moral values follow on from human nature and experience in some way. Humanists base their moral principles on reason (which leads them to reject the idea of any supernatural agency), on shared human values and respect for others.They believe that people should work together to improve the quality of life for all and make it more equitable.Humanism is a full philosophy, "life stance" or worldview, rather than being about one aspect of religion, knowledge, or politics.
"Non-religious" – as well as those who are uninterested in religion or who reject it, this category may include the vague or unaffiliated, those who are only nominally or culturally affiliated to a religious tradition, and the superstitious.
"Rationalist" in this context, describing a non-religious belief, means someone who prioritises the use of reason and considers reason crucial in investigating and understanding the world. Rationalists usually reject religion on the grounds that it is unreasonable. (Rationalism is in contradistinction to fideism – positions which rely on or advocate "faith" in some degree).
"Skeptic" today usually means someone who doubts the truth of religious and other supernatural or "paranormal" beliefs, typically on rationalist grounds. ('Skeptic' also has a special philosophical meaning: someone who rejects or is skeptical with regard to all claims to knowledge).
"Secularists" believe that laws and public institutions (for example, the education system) should be neutral as between alternative religions and beliefs. Almost all humanists are secularists, but religious believers may also take a secularist position which calls for freedom of belief, including the right to change belief and not to believe. Secularists seek to ensure that persons and organisations are neither privileged nor disadvantaged by virtue of their religion or lack of it. They believe secular laws – those that apply to all citizens – should be the product of a democratic process, and should not be determined, or unduly influenced, by religious leaders or religious texts. The word "secularism" was once used to describe a non-religious worldview generally but this meaning is now very old fashioned.
Definitions take from http://humanism.org.uk/humanism/humanism-today/non-religious-beliefs/