AnyObject

AnyObject can represent an instance of any class type.

1)
AnyObject can be used as the concrete type for an instance of any class, class type, or class-only protocol.
Example:

class TestB {}
var tmp1: AnyObject = TestB()
var tmp2: AnyObject = TestB.self

2)
AnyObject can also be used as the concrete type for an instance of a type that bridges to an Objective-C class. Many value types in Swift bridge to Objective-C counterparts, like String and Int.
Example:

var tmp: AnyObject = "This is a string" as NSString

Any

Any can represent an instance of any type at all, including function types, optional types.
Example:

var closure: () -> Void = {}
var tmp: Any = closure()

Ref:

https://medium.com/@mimicatcodes/any-vs-anyobject-in-swift-3-b1a8d3a02e00
https://developer.apple.com/documentation/swift/anyobject
https://docs.swift.org/swift-book/LanguageGuide/TypeCasting.html