According to the National Institutes of Health, a blastocyst is
a preimplantation embryo of about 150 cells produced by cell division following fertilization. The blastocyst is a sphere made up of an outer layer of cells (the trophoblast), a fluid-filled cavity (the blastocoel), and a cluster of cells on the interior (the inner cell mass).
So to rightly understand the use of the term blastocyst, we need to think not about what it is, but when and where it is. To answer the question: yes, a blastocyst is by its very definition an embryo, an embryo that has not yet implanted into the uterine wall, which is the distinction associated with the term 'preimplantation'. But the lack of implantation does not change the genetic makeup of the embryo, it simply is a geographical difference, not a logical or biological difference.
Be careful not to be confused by those who support the pursuit of embryonic stem cell research. I see them deliberately moving between the use of terms like 'blastocyst' and 'embryo'in order to create confusion because if you believe an embryo is a human being, but don't believe a blastocyst is yet an embryo, why would you object to this area of research?