style of voice
I guess the problem occurs when your voice has one sound, but you want it to have another.
Eg, you sound like Tiny Tim, but you want to sing like Bon Jovi!!!
If you accept the limitations of your own voice and write to suit it then you can be succesfull. eg Lou Read is not the world's most powerful singer, but hasn't stopped him having a career because his voice is distinctive and he writes FOR his own voice. Bob Dylan's another example.
If someone can hold a tune, then they can sing. It's then a matter of finding the right songs and style for that voice.
If you really can't hold a tune, then you've had it, period (ok I know there are lessons etc etc) but if it's that bad you're never gonna be a great vocalist.
If you can sing, but want to do a style of music for which your voice is not suitable, then you're into the business of having to get another singer to perform your work - frustrating!