Fundamentalism began as a movement within several Protestant denominations, in reaction to modernist or liberal tendencies within the mainstream Protestant churches, which sought to accomodate changing social attitudes, new scientific discoveries (evolutionary biology), and new scholarship about the origins of the Bible. Fundamentalists rejected the modernist or liberal tendencies as abandoning the core tenets of Christianity, and sought to return to the “fundamentals” of the faith, including fundamental doctrines of Western Christianity (the deity of Jesus Christ, the Resurrection, the Trinity) and of Protestant Christianity specifically (salvation by faith rather than works). The Fundamentalists also stressed the authority and inerrancy of the Bible, in a way that is specifically Protestant.
In addition to the specific Fundamentalist movement with a capital “F”, various other Protestant Christian groups (conservative Pentecostals or conservative Calvinists) may share a belief in Biblical inerrancy and other core doctrines, while disagreeing about the interpretation of what they all believe to be the inerrant Word of God. These groups may be called “fundamentalist” with a small “f”. Classically, capital-“F” Fundamentalists have not embraced speaking in tongues or other Pentecostal practices, have generally been premillenial (focusing on the end of the world as a sudden supernatural event), and were traditionally “separatist”, avoiding involvement in secular activities or institutions which were seen as worldly and corrupt, including politics. With the rise of the Religious Right, a segment of traditional Fundamentalists have become very much engaged in politics and the “culture wars”’; there has also been a softening of traditoinal lines between Pentecostals and non-Pentecostal Fundamentalists. Although most Religious Right Fundamentalists still very publicly embrace premillenialism (the Left Behind books), to some extent they no longer act like people who expect the world to end any minute, as they have invested a lot of time and energy in creating institutions here on Earth (media empires, universities, political action groups). For many, though, this is still all just part of the plan to evangelize the world in preparation for the Second Coming. Others may have drifted into a “postmillenialist” view, in which Christians will bring about the “Millennium” before the Second Coming, “Christianizing” the world by human (albeit, in their view, God-aided) effort.
Within a specific Protestant denominational family–Presbyterians or Baptists, for example–there may be “fundamentalist” or conservative denominations and more mainstream or liberal denominations, often tracing their roots back to some schism within an earlier denomination.
Jack Chick is defnitely a Protestant, and a I think a Fundamentalist of the old school as well–the claim that the King James Version is the only true English translation of the Bible is a hallmark of a certain school of American Fundamentalist Protestants. He definitely doesn’t like Catholics, and I don’t think he really likes the modern Religious Right movement in many ways, with its blurring of traditional intra-Protestant boundaries, and occasional tactical alliances with Catholicism. There has long been a tendency with some Protestants to form ostensibly ever-purer and in practice ever-smaller groups, splitting over various details of theology and practice. To achieve political power or social and cultural influence, that sort of focus on purity of doctrine tends to be a liability.