They sound very similar- is there a difference between them or are they interchangeable and pretty much mean the same thing?
In what sense/context do they sound the same?– rosendsJan 2, 2019 at 17:54
The Kollel Iyun HaDaf answers your question in its intro to Keritut 2 and lists a number of differences
Some sins are so severe that they are punished with untimely death. There are two types of untimely death that are used as heavenly punishments: Kares, and Misah b'Yedei Shamayim. Kares means "being severed" from the world and dying before one's time. Misah b'Yedei Shamayim means "death at the hands of heaven." These punishments are not administered by the courts, but through divinely administered justice.
One who deliberately transgresses a commandment that is punishable with either Kares or Misah b'Yedei Shamayim is punished even if there are no witnesses to his act, and even if he was not warned at that time of his transgression that his violation will result in his untimely death.
The commentaries explain that there are two major differences between Kares and Misah b'Yedei Shamayim (see Tosfos to Yevamos 2a DH Eshes Achiv; Rabeinu Yonah in Sha'arei Teshuvah, 3:6; Tiferes Yisrael to Sanhedrin 9:6):
One who is punished with Kares will die before age 60 (according to Moed Katan 28a, or before the age of 50, according to the Yerushalmi Bikurim 2:1). One punished with Misah b'Yedei Shamayim will die after the age of 60 but before his time has come (according to Moed Katan ibid., or before the age of 60, according to the Yerushalmi ibid.)
When one is punished with Kares, even his children (who are minors at the time of his sin) die, and he bears no further children. When one is punished with Misah b'Yedei Shamayim, only he is punished and not his children (Yevamos 55a and Rashi there). (See, however, Riva in Tosfos to Yevamos 2a DH Eshes, who maintains that Kares only involves the death of one's children in the two cases where the Torah adds the word "Ariri." However, he might be referring to the death of children who are not minors.)
Some add that when punished with Kares, the sinner's cattle and possessions slowly expire until he is left destitute -- see Insights to Yevamos 73:2.
For a number of specific sins, the Torah assigns a form of Kares in which the sinner not only dies before his time but is not granted a portion in the World to Come (Sanhedrin 64b, 90b).
1interesting point about the children. Why should they suffer on the sins of the father? Jan 2, 2019 at 22:12
1@mbloch such a thorough response- shkoyach and thanks for answering!– alichtJan 2, 2019 at 22:23
According to Rashi Kares can fall on the children of the offender and only occurs at the offenders half way point through life. The Ibn Ezra (Breshis 17,14)says before 25 years old is kares. The Rambam seems to say that Kares only hurts a person on this world. My source https://he.wikipedia.org/wiki/%D7%9B%D7%A8%D7%AA#%D7%94%D7%94%D7%91%D7%93%D7%9C_%D7%91%D7%99%D7%9F_%D7%9B%D7%A8%D7%AA_%D7%9C%D7%9E%D7%99%D7%AA%D7%94_%D7%91%D7%99%D7%93%D7%99_%D7%A9%D7%9E%D7%99%D7%9D