The difference between implicit conversion and explicit is just syntactic sugar: do you have to put some visible tokens into the code to allow a conversion to happen, or not.
Implicit conversion can be seen as the compiler deciding among several possible conversions (or possibly just one) and inserting the coercion/casting operator into the intermediate code to make it happen.
(Of course, this can be a run-time decision based on dynamic types also, but the reasoning is the same. E.g. the run-time sees that a plus operation is adding an integer and float, and can either signal an error (requiring the program to be repaired by inserting a conversion operation into the expression), or just do that conversion, like the integer operand to float.
It's the other way around. Implicit conversion is syntactic sugar for explicit conversion. Sugar is anything that is functionally identical, just notated more conveniently.
That said, I think you're correct about the casting versus conversion distinction. Languages frequently overload established terminology with slightly modified variants and it's incredibly confusing.
Implicit conversion can be seen as the compiler deciding among several possible conversions (or possibly just one) and inserting the coercion/casting operator into the intermediate code to make it happen.
(Of course, this can be a run-time decision based on dynamic types also, but the reasoning is the same. E.g. the run-time sees that a plus operation is adding an integer and float, and can either signal an error (requiring the program to be repaired by inserting a conversion operation into the expression), or just do that conversion, like the integer operand to float.