  Let $p$ be an odd prime. We attach appropriate signed Selmer groups to an
elliptic curve $E$, where $E$ is assumed to have semistable reduction at all
primes above $p$. We then compare the Iwasawa $\lambda$-invariants of these
signed Selmer groups for two congruent elliptic curves over the cyclotomic
$\mathbb{Z}_p$-extension in the spirit of Greenberg-Vatsal and B. D. Kim. As an
application of our comparsion formula, we show that if the $p$-parity
conjecture is true for one of the congruent elliptic curves, then it is also
true for the other elliptic curve. In the midst of proving this latter result,
we also generalize an observation of Hatley on the parity of the signed Selmer
groups.
