There's many differences.
And airplane mode is not silent mode. Far from it.
With airplane mode texts, calls, imessages, emails nothing will come in and you will have no idea even if anyone tried calling you.
If its on silent at least you can see if anyone called, texted, who, what time etc...
There is a big difference if it's in airplane mode then all the radios are disabled so you won't receive any alerts. With Do Not Disturb you still receive alerts your phone just doesn't make you aware of them in most circumstances, but will still let calls through from favourites or in an emergency if they call twice in 3 minutes