As soon as a sperm fertilizes an egg, a unique human being is formed. The DNA which determines every feature from hair and eye color to height is fully present at the MOMENT of conception. There are different terms used to describe a unique human life prior to birth including zygote, blastocyst, embryo, and fetus just as we use the terms infant, toddler, preschooler, teenager, etc. to describe different stages of life once a human is born.
Most organs are fully formed at around 10 weeks after fertilization. This excludes the brain and spinal cord which continue to grow throughout the remainder of the pregnancy.