  Extreme excesses of $^{13}C$ ($^{12}C$/$^{13}C$<10) and $^{15}N$
($^{14}N$/$^{15}N$<20) in rare presolar SiC grains have been considered
diagnostic of an origin in classical novae, though an origin in core collapse
supernovae (CCSNe) has also been proposed. We report C, N, and Si isotope data
for 14 submicron- to micron-sized $^{13}C$- and $^{15}N$-enriched presolar SiC
grains ($^{12}C$/$^{13}C$<16 and $^{14}N$/$^{15}N$<~100) from Murchison, and
their correlated Mg-Al, S, and Ca-Ti isotope data when available. These grains
are enriched in $^{13}C$ and $^{15}N$, but with quite diverse Si isotopic
signatures. Four grains with $^{29,30}Si$ excesses similar to those of type C
SiC grains likely came from CCSNe, which experienced explosive H burning
occurred during explosions. The independent coexistence of proton- and
neutron-capture isotopic signatures in these grains strongly supports
heterogeneous H ingestion into the He shell in pre-supernovae. Two of the seven
putative nova grains with $^{30}Si$ excesses and $^{29}Si$ depletions show
lower-than-solar $^{34}S$/$^{32}S$ ratios that cannot be explained by classical
nova nucleosynthetic models. We discuss these signatures within the CCSN
scenario. For the remaining five putative nova grains, both nova and supernova
origins are viable because explosive H burning in the two stellar sites could
result in quite similar proton-capture isotopic signatures. Three of the grains
are sub-type AB grains that are also $^{13}C$ enriched, but have a range of
higher $^{14}N$/$^{15}N$. We found that $^{15}N$-enriched AB grains
(~50<$^{14}N$/$^{15}N$<~100) have distinctive isotopic signatures compared to
putative nova grains, such as higher $^{14}N$/$^{15}N$, lower
$^{26}Al$/$^{27}Al$, and lack of $^{30}Si$ excess, indicating weaker
proton-capture nucleosynthetic environments.
