What is the difference between private and fileprivate in Swift 4

File Private
File-private access restricts the use of an entity to its own defining source file. Use file-private access to hide the implementation details of a specific piece of functionality when those details are used within an entire file.
Syntax: fileprivate <var type> <variable name>
Example: fileprivate class SomeFilePrivateClass {}

Private
Private access restricts the use of an entity to the enclosing declaration, and to extensions of that declaration that are in the same file. Use private access to hide the implementation details of a specific piece of functionality when those details are used only within a single declaration.
Syntax: private <var type> <variable name>
Example: private class SomePrivateClass {}

Here is more detail about all access levels: Swift - Access Levels

Answer to your question: (In Swift 3, private variables in a class are not visible in its extensions in the same file. For that, fileprivate had to be used.)

Yes, in Swift 4.0, Private is now accessible in extension but within same file. If you declare/define extension in other file, then your private variable will not be accessible to your extension

Look at this images:
File: ViewController.swift
Here extension and view controller both are in same file, hence private variable testPrivateAccessLevel is accessible in extension

File: TestFile.swift
Here extension and view controller both are in different files, hence private variable testPrivateAccessLevel is not accessible in extension.

Here class ViewController2 is a subclass of ViewController and both are in same file. Here private variable testPrivateAccessLevel is not accessible in Subclass but fileprivate is accessible in subclass.

Applicable in swift 4.0 and its versions
Private
Private access only in class and its extension(When extension is in the same .swift file).

File Private
File-private access only in class and its extension & subClass(When extension or subClass is in the same .swift file).

///////////////ViewController1.swift file
        class ViewController1 {
            private func testPrivate() {
                print("testPrivate")
            }
            fileprivate func testFilePrivate() {
                print("testFilePrivate")
            }
            func doesNothing1() {
                testPrivate() //success
                testFilePrivate() //success
            }
        }
        extension ViewController1 {
            func doesNothingInExtensionSameFile() {
                testPrivate() //success
                testFilePrivate() //success
            }
        }
        class SomeOtherClassInSameFile {
            let vc1 = ViewController1()
            func doesNothing() {
               vc1.testPrivate() //throws error
               vc1.testFilePrivate() //success
            } 
        }
////////////// ViewController2.swift file
        extension ViewController1 {
            func doesNothingInExtensionDifferentFile() {
                testPrivate() //throws error
                testFilePrivate() //throws error
            }
        }

private and fileprivate access levels have come closer with Swift4.

The difference in access lies as follows:

fileprivate members - only & entirely within that .swift file

private members - only in that class & extension of the class if both are present in same .swift file

Hence only fileprivate members(not private) can be accessed in

• Sub Classes in the same .swift file
• Instances of the class (initialized in another class) in the same .swift file.

Open Vs Public:

• Public does not allow a class to be inherited in another module/target whereas Open does.
• Public method does not allow to be overridden in subclass in another module/target whereas Open does.

Apart from above both are same.

Private Vs Fileprivate:

• (Within single file) Private does not allow to access (func and properties) in subclass whereas FilePrivate does.
• (Outside File) Private and FilePrivate both can't be accessible.

Apart from above both are same.

"Private" is accessible only in class, "FilePrivate" accessible only in .swift file.

Private : Access in Class and Class Extension. FilePrivate : Access in class, subClass, Extension,