Praise be to Allah.
The blood which may be passed during pregnancy may be menstrual blood, or it may be irregular vaginal bleeding, or it may be the blood of Nifas. It is the blood of Nifas if it comes at the time of labour contractions. Some of the scholars said (that it is the blood of Nifas) even if it comes two or three days before delivery.
Shaykh Al-Islam (may Allah have mercy on him) said:
“With regard to that (blood) which is seen two or three days before delivery, it is Nifas, because it is blood that comes out because of giving birth, so it is Nifas just like blood that comes out afterwards. This is because pregnant women rarely see blood, but if a pregnant woman sees blood close to the time of delivery, it is obviously because of birth, especially if she is having contractions.” (Sharh Al-`Umdah, 1/514, 515)
It is menstrual blood if it has the characteristics of menstrual blood and comes at the time when she usually menstruates. This is the view favoured by Shaykh Muhammad ibn Ibrahim and Ibn `Uthaymin (may Allah have mercy on them). (See Fatawa Muhammad ibn Ibrahim, 2/97)
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
“If a pregnant woman experiences persistent bleeding that comes at the time of the month when she usually menstruates and looks like menstrual blood, then it is most likely to be menstruation and she should stop praying, fasting etc, because of that. The only difference with regular menstrual blood is that it has no bearing on the `Iddah [in case of divorce or widowhood], because pregnancy is the stronger factor in that case.” (Ash-Sharh Al-Mumti`, 1/405)
The view that a pregnant woman may menstruate is the view of Ash-Shafi`i (may Allah have mercy on him) and was narrated in one report from Ahmad (may Allah have mercy on him); it was also the view favoured by Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him), as stated in Al-Ikhtiyarat, p. 59; but it is very rare for pregnant women to menstruate.
It is irregular vaginal bleeding if it is something other than that described above (i.e., menstruation or Nifas); this is red blood that is discharged in the case of Istihadah (irregular bleeding outside menses). This is what some women call haemorrhage.
This does not mean that a woman should not pray or fast; rather she comes under the same rulings as women who are pure (i.e., not menstruating). (Fatawa Ash-Shaykh Ibn `Uthaymin, 2/270)
This third category is what applies in the case mentioned in the question, because these drops of blood are not menstruation and do not mean that a woman should stop praying and fasting , and she does not come under the rulings on menstruation.
And Allah knows best.