Q:

Is there a difference between "kareis" and "misas be'dei shamayim?"

They sound very similar- is there a difference between them or are they interchangeable and pretty much mean the same thing?

A:

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).

For further research see also here and there

