Failling pregnancy is determined by beta HCG levels which tends to go down with a positive pregnancy sac in in uterus chemical pregnancy is there will be beta HCG values which is positive but you cannot see pregnancy in ultrasound scan either intrauterine or extrauterine also. Is also ultimately tries to goes down Missed abortion is after the baby is identified with heart rate and it is stopped later on pregnancy progress especially in early pregnancy

Failing pregnancy or miscarriage means the levels of hcg or progesterone are not sufficient enough to sustain the pregnancy which leads to failure . The other reason might be chromosomal abnormalities in the fetus which can lead to miscarriage. Missed abortion  is when even at 6 or 7 weeks , fetus doesnt have a heart beat or loses its heart beat eventhough it had a normal heart beat previously. Chemical pregnancy is when hcg levels come in the levels seen in pregnancy but patient has spontaneous bleeding around the time of expected menses. But upt positive in some cases.