Basically, both sides are going by the definition of abortion as "deliberately ending a pregnancy, either surgically or chemically." Both groups believe that pregnancy only
naturally ends through either birth or miscarriage.
The difference is where they define the beginning of pregnancy.
The official, scientific definition is that pregnancy begins when the embryo (usually in the blastocyst stage) implants in the uterine wall (generally about a week after conception). The "pro-life" definition is that pregnancy begins at the moment of conception, because this is when a genetically distinct organism first makes the scene.
This revisionist definition has the effect of classifying any post-coital birth control that prevents implantation as abortifacient, even though it isn't by medical definition.
This discrepancy in the beginning point of pregnancy is probably also the source of my least-favorite abortion propaganda:
The embryo's (two-chambered) heart begins to beat about 3 weeks after the beginning of pregnancy (scientific definition); in other words, 4 weeks after the baby is conceived. A Beka's textbooks are surprisingly accurate on this score, given the publisher's tendency to ignore facts that do not suit its agenda. However, a lot of billboards use the "pregnancy begins at conception" idea to sell the tripe you see above. 18 days < 3 weeks. An embryo 3 weeks post-conception generally is just beginning to develop the spinal cord and a primitive heart tube. The heart does not yet have any chambers and thus cannot beat.
Besides, born humans don't have two heart chambers--fish do. We have four-chambered hearts. The anti-abortion crowd NEVER mentions that the embryo's heart is dramatically different from what it will become over the course of its prenatal development, because they want to push the idea that an embryo already looks like a born baby. This is also why a six-week-old embryo (dated from conception) is often deliberately mislabeled as being a four-week-old embryo (again, dated from conception); at four weeks, an embryo doesn't look recognizably human yet, and that simply
will not do.