texting problem.

Last night I sent a text to my wife and it shows it was sent in my message app but she didn't get it. Today I sent a text to my son and it shows as sent in my message app but he didn't get it. Could this be a phone issue? Never experienced this with my previous smartphone.
 
I had a similar issue occasionally on my Cosmos 2 (not a smartphone by any means). The messages would show up on my phone as not sent but the other person would respond so they had most definitely been getting them.