In my mind (let anyone who reads this remember that I'm only speaking for egoism as is know in politics and writing) there are two main types of egoism: The most popular variety is mostly associated with the idea that nature is a war of all-against-all, and selfishness is an idealized personal trait. I would say that Ayn Rand is the poster child for this type of egoism. Ayn Rand takes this a step further and idealizes competition (since nature is a brutal competition of all against all), and claims that free market capitalism is the best form of relation that man can hope for.
The other variety of egoism stems from Max Stirner, and fueled the writing of the books that dot mentioned. Without including the philosphical jargon that he used as a student of philosophy, Max Stirner's egoism rejects the subordination of the individual to any group or concept. During his time period (the mid 1800's), he was directly opposing the fact that philosophers were fixated on concepts that were external and alien to all breathing, eating, shitting individuals such as God, "the people", and morality. Stirner's egoism is ruthless in the sense that it sees nothing as being above any individual. This is drastically different from the egoism of Ayn Rand and co., which sees capitalism as the height of progress and the superior form of social relation to any other political system like communism or socialism.
If you read "The Unique and It's Property", it becomes pretty clear that Stirner has a suspicion with a self-identification with anything, I've read about 90 pages of it and there are several sections where he likens the process of identifying with something other than yourself as being religious (the term "religion" having it's linguistic roots in latin to being bound).