The main thing to notice here is that there are two main textual traditions in Leviticus, the so-called “Priestly Torah” and the so-called “Holiness School.” “P” material is focused primarily in chapters 1-16 and “H” material is found mostly but not only in chapters 17-26. There are many ways in which the conceptual world and specific ritual rules of P and H are different.
In this particular case, there is no obvious explanation for some laws are different when they are the exact same (Ex: Leviticus 20:18; 15:24), though many theories. Here is Jacob Milgrom’s comment on 20:18 in the Anchor Bible. Notice that he interprets karet as capital punishment to be enacted by divine justice, so neither banishment or a judicidally-enacted capital punishment, but something handled by God.
In the NOTE on 15:24, I suggested that the reason P declares the man impure for seven days if he engages in sex with a menstruant, but impure for only one day in all other sexual liaisons (15:18), is that loss of life is symbolically oozing out of both partners. Or, sex during this period cannot lead to conception (Eilberg-Schwartz 1990: 182–85; Biale 1992:28:31). It does not, however, explain why H regards the copulative act as a capital crime (by the divine court) warranting kārēt. The answer may lie in the designation of the menstruant as dāwâ ‘infirm’ (20:18; cf. Lam 1:13; 5:17) and her condition as niddat dĕwōtāh ‘her menstrual infirmity’ (12:2). That is, by imposing such a drastic penalty, H is creating a deterrent that will protect the woman from unwanted advances by her husband during her period of weakness (R. Gane). This explanation would therefore coincide with the overall rationale behind the entire list of forbidden sexual unions—to prevent the family head (the addressee) and other dominant males from taking advantage of the woman. Thus sex during her physical infirmity (menstruation) is a symbol of sex during her figurative infirmity, if widowed or divorced and a vulnerable prey to the males in her household (see NOTE on 18:7 [Ziskind 1988]).
[Lev 17-22, p. 1756]
It might be thought that the reason that P (15:24) prescribes seven days of impurity, whereas H (20:18) prescribes kārēt, is that P deals with inadvertences and H deals with advertences (R. Gane). It is more likely, however, following Abravanel (see NOTE on 15:24), that P is concerned with the nature of the generated impurity, not with its penalties. Indeed, certain acts described in chap. 15 are clearly deliberate (e.g., sex! v. 18). Indeed, intention plays no part whatsoever in chap. 15; whether advertent or inadvertent, they generate impurity. Chap. 20, however, focusing solely on sexual intercourse, is limited to advertences.
Leviticus 20:18 is part of the so called “Holiness Code”, which differs from the rest of Leviticus in some respects. So it is indeed a contradiction if one expects the text to be unified. So generally speaking you will see contradictions like as Leviticus 20 is part of the Holiness Code, or Holiness Torah. Leviticus 15, on the other hand, is part of the Priestly Torah.