This is one of the 21st centuries most unnoticed mysteries, the two different iPhone incoming call screens. Sometimes you’re given the option to either answer or decline the call, while other times you only have the option to “slide to answer”.
Even though I had noticed this before, by the time the call was over I had forgotten all over the mysterious riddle and moved on with my life. However, today I snooped around for an answer and found one.
The two incoming call screens of the iPhone. Source
If you receive a call while your phone is locked, your phone will only display the “slide to answer” incoming call screen. To get the option to decline the call, you’ll have to double tap the power button on the top right side of your phone.
However, if your phone is unlocked you’ll receive a totally different incoming call screen – one with both options to “accept” or to “decline” the call.
Either way, you can still perform all other actions – set a reminder to call back, send a text message, etc. – no matter if your iPhone is locked or not.