What is the difference between typecasting and typeconversion in C++ or Java ?
Type casting is treating a value (block of memory) referenced by a variable as being of a different type than the type the variable is declared as.
Type conversion is actually performing a conversion of that value.
In many languages, some casts (usually numeric ones) do result in conversions (this will vary quite a bit by language), but mostly it's just "treat this X as a Y".
Like most aspects of human language, unfortunately the terms are used slightly differently in different communities, mostly along language lines. For instance, see James' comment below about C++ — the word "cast" there has a much broader meaning than the above definition, which is more in the C or Java mold. And just to make things fun, the Java Language Spec actually gets into various kinds of casts, including casting conversions. But the above is a good rule of thumb.
But to take a simple case:
In Java, prior to generics it wasn't unusual to have to do a lot of typecasting when dealing with maps:
Map m = new HashMap();
m.put("one", "uno");
// This would give a compiler error, because although we know
// we'll get a String back, all the compiler knows is that it's
// an Object
String italian = m.get("one");
// This works, we're telling the compiler "trust me, it's a String"
String italian = (String)m.get("one");
Fortunately, the addition of generics addressed this, as casting in this way tends to be a fragile process with maintenance issues.
In contrast, you'd convert if you had a String of digits:
String s = "1234";
...and needed to know what number those digits represented in decimal:
// Wrong (cast)
int n = (int)s;
// Right (conversion)
int n = Integer.parseInt(s, 10);