On Kidushin 61A Rashi uses two terms: in D'H Nehi Dbahadei Karka lo Kadshei Rashi uses the term 'Kataprass' - [are the vowels correct?] and in D'H Nikdshu Beapei Nafshaihu - the term 'Midron'.
What are the exact meanings of and differences between the terms?
They both mean incline, "Katafras" being Greek. In general, however, linguistically "Midron" is used to mean the incline itself while "Katafras" is often used to represent things which move along the incline such as in "ha'Nitzok v'ha'Katafras" (our Gemara's use of the term is obviously an exception).
(Perhaps the word "Midron" might be the word that is used when referring to the the incline from the perspective of the bottom (the incline of the pit from the perspective of one standing at the base of the pit); i.e. an upward incline. "Katafras" is used when referring to a downward incline (the incline of the pit from the perspective of one standing in the field). This would seem to be corroborated by the usage of the words elsewhere (see Rash, Taharos, end of Perek 8; Rashi, Eruvin 19b, 35a, 57b).) (E. Kornfeld, Y. Shaw)
(It seems that Rashi's intention here, in using the different words, is as follows. Rashi wants to point out that the Gemara is saying that, granted, we do not measure the length of the slope as part of the field; this length of the slope is what Rashi refers to as the "Katafras." But we should at least measure the width of the pit (from one edge to the other) as if it had no slope; in this manner we do not ignore the area of the slope altogether (and just count the flat floor of the pit), but rather we count the width of the pit as if it were all flat land. That is why Rashi writes that we should not count the "Midron," meaning the amount of distance that the slope adds when measuring the sloping walls and floor of the pit.) (M. Kornfeld)