Different people use it to mean different things. It need not be true outside .net world, but here is what I have understood in .net context reading Eric Lippert's blogs:
All transformations of types from one form to another can be called conversion. One way of categorizing may be
implicit -
a. representation changing (also called coercion)
int i = 0;
double d = i;
object o = i; // (specifically called boxing conversion)
IConvertible o = i; // (specifically called boxing conversion)
Requires implicit conversion operator, conversion always succeeds (implicit conversion operator should never throw), changes the referential identity of the object being converted.
b. representation preserving (also called implicit reference conversion)
string s = "";
object o = s;
IList l = new List();
Only valid for reference types, never changes the referential identity of the object being converted, conversion always succeeds, guaranteed at compile time, no runtime checks.
explicit (also called casting) -
a. representation changing
int i = 0;
enum e = (enum)i;
object o = i;
i = (int)o; // (specifically called unboxing conversion)
Requires explicit conversion operator, changes the referential identity of the object being converted, conversion may or may not succeed, does runtime check for compatibility.
b. representation preserving (also called explicit reference conversion)
object o = "";
string s = (string)o;
Only valid for reference types, never changes the referential identity of the object being converted, conversion may or may not succeed, does runtime check for compatibility.
While conversions are language level constructs, Parse is a vastly different thing in the sense it's framework level, or in other words they are custom methods written to get an output from an input, like int.Parse which takes in a string and returns an int.
