"3. By preventing an embryo from implanting into the uterus.
Which of the contraceptives mentioned in this article fall into the third category?"
Briefly, ALL oral contraceptives can, however it is difficult to estimate how often because the abortion happens before a woman would have a positive pregnancy test. The oral contraceptives used nowadays are more likely to be an abortifacient than when they first came out on the market. This is because when they first came out they used higher doses which were more likely to prevent ovulation. Unfortunately the higher dose pills were found to cause cancer. The "lower dose" contraceptives in use today are less likely to cause cancer but are also less likely to prevent ovulation and are more likely to be abortifacients.
Other categories such as IUD's (Intrauterine Devices) do not prevent ovulation and work almost soley as abortifacients. The only contraceptives that I know of that would not be abortifacient would be barrier methods or perhaps? spermicides (although I'm not sure about the latter).
There is a group of prolife OB's who disagrees about Oral contraceptives being abortifacient, however having reviewed the literature, the research they cite is misleading and pretty shoddy work.
If you go to the couple to couple league's website they have a good article on it with resources at the end.
http://www.ccli.org/contraception/Abortifacients.shtml
Having said that, an informed, faithful Catholic would have moral problems selling contraception regardless of whether it was an abortifacient or not.
The writer of the text behind that link seems obsessed with the endometrial-lining and the fact that it changes thickness. That is a natural outcome of menstruation dating back to menarche. The lining is shed every month and therefore, whether a woman is on or off the pill, it changes size during it's 28 day 'life'. I appreciate your viewpoint, I'm going to have to file the 'BC pill is abortion' story with the 'they're out to get us with fluoride in the water' hysteria.