Conception is a noun. Early 14c., "act of conceiving," from Old French concepcion and while the word can refer to, the act of conceiving, as in giving birth (see conceive). The word also is derived from Latin, conceptionem (nominative conceptio) "a comprehending, conception," noun of action from stem of concipere.
Originally in the womb sense (also with reference to Conception Day in the Church calendar); mental sense "process of forming concepts" is late 14c. Meaning "that which is conceived in the mind" is from 1520s; "general notion" is from 1785.
Inception refers to, early 15c., "beginning, starting," from Middle French incepcion and directly from Latin inceptionem (nominative inceptio) "a beginning, undertaking," noun of action from past participle stem of incipere "begin, take in hand," from in- "in, on" (see in- (2)) + cipere comb. form of capere "take, seize" (see capable).
Source: Various Etymology Dictionaries.