Yes, Please do not attempt to buy an iPhone 5 LCD assembly expecting to be able and use it on an iPhone 5C.
The connectors to the mother board are different.
On the iPhone 5, both the LCD and Digitizer connectors are horizontal.
Versus the iPhone 5C;
The digitizer connector is vertical. The LCD connector is horizontal. And, on both the iPhone 5 and iPhone 5c, the front camera flex cable is also vertical.
The iPhone 5 and iPhone 5C are NOT identical.