doc: remove style, update callbackify

doc/api/errors.md

@@ -128,12 +128,12 @@ they are thrown *after* the calling code has already exited.
 Developers must refer to the documentation for each method to determine
 exactly how errors raised by those methods are propagated.
 
-### Error-first style callbacks
+### Error-first callbacks
 
 <!--type=misc-->
 
 Most asynchronous methods exposed by the Node.js core API follow an idiomatic
-pattern  referred to as an "error-first style callback". With this pattern, a
+pattern  referred to as an _error-first callback_. With this pattern, a
 callback function is passed to the method as an argument. When the operation
 either completes or an error is raised, the callback function is called with
 the Error object (if any) passed as the first argument. If no error was raised,
@@ -156,7 +156,7 @@ fs.readFile('/some/file/that/does-exist', errorFirstStyleCallback);
 
 The JavaScript `try / catch` mechanism **cannot** be used to intercept errors
 generated by asynchronous APIs.  A common mistake for beginners is to try to
-use `throw` inside an error-first style callback:
+use `throw` inside an error-first callback:
 
 ```js
 // THIS WILL NOT WORK:

doc/api/util.md

@@ -21,9 +21,10 @@ added: v8.2.0
 * Returns: {Function} a callback style function
 
 Takes an `async` function (or a function that returns a Promise) and returns a
-function following the Node.js error first callback style. In the callback, the
-first argument will be the rejection reason (or `null` if the Promise resolved),
-and the second argument will be the resolved value.
+function following the error-first callback style, i.e. taking
+a `(err, value) => ...` callback as the last argument. In the callback, the
+first argument will be the rejection reason (or `null` if the Promise
+resolved), and the second argument will be the resolved value.
 
 For example:
 
@@ -517,8 +518,8 @@ added: v8.0.0
 * `original` {Function}
 * Returns: {Function}
 
-Takes a function following the common error-first style callback, i.e. taking a
-`(err, value) => ...` callback as the last argument, and returns a version
+Takes a function following the common error-first callback style, i.e. taking
+a `(err, value) => ...` callback as the last argument, and returns a version
 that returns promises.
 
 For example:
@@ -555,7 +556,7 @@ will return its value, see [Custom promisified functions][].
 `promisify()` assumes that `original` is a function taking a callback as its
 final argument in all cases. If `original` is not a function, `promisify()`
 will throw an error. If `original` is a function but its last argument is not 
-an error-first style callback, it will still be passed an error-first style 
+an error-first callback, it will still be passed an error-first
 callback as its last argument.
 
 ### Custom promisified functions