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Last updated at 1:57 pm UTC on 3 February 2020
As far as Squeak is concerned 'Smalltalk' has two meanings:

First meaning

The usual meaning of "Smalltalk" is either the Squeak programming language or the historical programming environment that Squeak derives from. Note that the "t" in Smalltalk isn't capitalized and there is no space between Small and talk.

Smalltalk is the programming language of the Dynabook (as explained in Personal Dynamic Media).

From the preface of the Blue Book

Squeak is a descendent of Smalltalk-80. The core developers of Squeak (then named Squeak Central) in fact included many of the core developers of Smalltalk-80.

Squeak's language and much of the core class library is identical to that of Smalltalk-80: they both have objects, classes, single inheritance, blocks, garbage collections, collections, streams, model-view-controller, and many other bits. In the meantime the class library has been extended considerably.

ANSI Smalltalk is a recognized standard for Smalltalk. While Squeak is Smalltalk in spirit, it is not fully compliant with the ANSI Smalltalk standard. There is temporarily an add-on on SqueakMap which tries to move Squeak towards ANSI compatibility.

Also see:

Second meaning

Smalltalk is a well known global variable within the image.

After the environments changes in March 2017 (called 'Squeak 6.0alpha' at that time) references to it have to be replaced.

More see Smalltalk global variable