C function vs. Objective-C method?

Actually, an Objective-C method is just a C function with two arguments always present at the beginning.

This:

-(void)aMethod;

Is exactly equivalent to this:

void function(id self, SEL _cmd);

Objective-C's messaging is such that this:

[someObject aMethod];

Is exactly equivalent to this (almost -- there is a variadic argument ABI issue beyond the scope of this answer):

objc_msgSend(someObject, @selector(aMethod));

objc_msgSend() finds the appropriate implementation of the method (by looking it up on someObject) and then, through the magic of a tail call optimization, jumps to the implementation of the method which, for all intents and purposes, works exactly like a C function call that looks like this:

function(someObject, @selector(aMethod));

Quite literally, Objective-C was originally implemented as nothing but a C preprocessor. Anything you can do in Objective-C could be rewritten as straight C.

Doing so, however, would be a complete pain in the ass and not worth your time beyond the incredibly educational experience of doing so.

In general, you use Objective-C methods when talking to objects and function when working with straight C goop. Given that pretty much all of Mac OS X and iOS provide Objective-C APIs -- certainly entirely so for the UI level programming entry points -- then you use Obj-C most of the time.

Even when writing your own model level code that is relatively standalone, you'll typically use Objective-C simply because it provides a very natural glue between state/data & functionality, a fundamental tenant of object oriented programming.

In Objective-C each function operates on an object, like

[myObject myFunction]

A C method has the form:

return-type function-name(argument1, argument2, etc) {}

An Objective-C instance method has the form:

-(return-type)function-name:argument1 {}

or for a multi-argument function

-(return-type)function-name:argument1 function-name:argument2 {}

I always use Objective-C-style methods in Obj-C programming, even though you can still use C-type functions as well.

I suppose the equivalent in C to [myObject myMethod:arg] might be myObject.myMethod(arg)

The first is a freestanding function. The second is an instance method for an Objective-C class. So I guess you would need the second version if you're actually writing a class.