All the chargers from different makes provide USB interface which is then converted to lightning connector.
Since USB standard is common for all, there should not be any problem in interchanging chargers of different makes. At least this should be valid for iPhone (this thread does not pertain to other makes)
I assume you are talking about the wall plug portion and not the cable. Yes, they should all "work", however there could be a problem with amperage...some of them come in different amp ratings. I have a Samsung bluetooth at one point in the past, the walk plug for that one is .2 amps...... The power draw of a running device is likely to be greater than that, meaning, it will never achieve a full charge. I believe the one that came with the HTC Touch Pro2 was .5 amps....and will charge a device much slower than the stock charger. On the other hand, I believe the one that came with my wife's first iPad, (looked like a mini version of the MacBook charger, was 1.5 Amps....and will charge very fast.
The one in my Honda is .25 amps, and if my phone is being used, the iPhone 7 Plus does not charge completely during a 300 mile trip... It is very frustrating, so I bought an Anker, which chargers at 2.5 amps, and charges very quick.
So yes, while any usb wall adaptor, or cig adapter, may work, I would not agree that "there should not be any problem."
If you want a more coherent explanation, there is this website, it looks a bit dated, but still the information should be the same.
http://www.righto.com/2012/10/a-dozen-usb-chargers-in-lab-apple-is.html
