That depends on your texting plan.  if you have no texting package, then you are charged per message sent and received.  The $5 for 250 texts does not have any provision for Verizon to Verizon texts, every text sent or received is counted.

Texting plans above the $5 plan all include Verizon to Verizon unlimited texting.

$5/mo for 250 texts (sent and received)
$10/mo for 500 texts PLUS unlimited texts M2M
$20/mo for 5000 texts PLUS unlimited M2M

If you are on a Talk and Text plan, then you have unlimited texting to any carrier.

Hope this answers your question.