Audio playback through iPhone 4S speaker & attached headphones

Question

Hi!
I might have a problem and I definitely need help, please!
When I first got my iPhone 4S, I remember seeing an option... I was able to switch between the earphones and the speaker while listening to music (while headphones still attached, of course) and this was amazing since I listen to music all day but I don't want to keep attaching/removing the headphones over and over again. I remember playing with my iPhone and seeing an option to turn this amazing feature off (I did this while playing with multitasking), and I remember that I did change it to "earphones" or something, just out of curiosity, thinking that I could always change the settings to the way it was but now, I can't get it back!
I've read manuals, guides, reviews and I've only found information about this feature but no information about how to actually do it (again)
This has nothing to do with AirPlay, Bluetooth and/or Wireless speakers (nor Siri and Voice Control, I think)
So, I was able to switch between earphones and speakers while my earphones still attached but now that on-screen option is gone, I don't see that anymore. It was something similar to this, actually...

Answer 1

Well, I called the Apple support line and explained the whole thing but since I used the image as an example and I mentioned speakers, the guy helping me focused on wifi speakers and didn't really understand my problem; he thought it was something else.
Since then I've done some research and I've even reseted my iPhone twice but still not able to make it work again. I am not lying and I am not crazy (well, that's a different topic ) ... I remember seeing an image just like the one I linked on this post. This whole thing happened on a 64 GB iPhone 4S... no jailbreak or whatever, I don't even understand that thing so, yes, brand new, 100% original iPhone, untouched
Ok, so... I was listening to music, I had the headphones plugged in and I remember pressing a small square-like button, then 2 options showed on-screen; headphones and speaker, and I was able to select one and then go back to the other, switch between both headphones and the built-in speaker, while the headphones were still plugged in, of course.
The problem presented when I double clicked the home button (while multitasking) and then selected an option (right where the volume controls are located) and it was something like "always use headphone", "always use speaker" or something similar and then I selected headphones while I was playing music via the speaker and that was it, I haven't been able to "swap" since I changed that... so yes, I know it was possible because I've done it
Honestly, I am starting to think that my iPhone was not 100% configured or something and that's why I was able to do so.... and then pressed something by mistake which "corrected" that malfunction.
Anyway, thank you for the help Josephack, I appreciate it!