Smalltalk is an incredibly compact language and remains one of the purest object oriented languages. Objective-C is a pragmatic compromise between Smalltalk and C, which leads to some very significant differences. For example, in Smalltalk, all this is an object - even prime numbers - and each manipulation of the object is done by sending a message. Messages are evaluated in the same order, regardless of their name. So, for example, the following:
8 + 9 / 23 + 16 * 8
It is evaluated in strict order from left to right, because the operators '+', '/' and '*' do not have much meaning for the language, which is just messages transmitted to numeric objects.
Objective-C adds Smalltalk-style objects to C, but is also a strict superset of C that preserves C primitive types and built-in operators. Thus, in Objective-C, the normal mathematical order of operations will be applied to the expression above - division and multiplication will be performed first, additions later.
Learning C is absolutely essential for a deep understanding of Objective-C. Objective-C is a strict superset of C and explicitly uses exactly the same syntax and semantics as possible. He transplants the concept of objects in C because of the ability of C to hold a pointer to a thing, not knowing how to apply any operations to an object. He then extends C syntax to provide means for sending messages to objects and for declaring and implementing messages that an object can receive.
Most of the overall design of the Objective-C runtime, especially in conjunction with Cocoa, comes directly from Smalltalk, including the concept of a selector, the use of metaclasses as factories for class instances, hierarchies and inheritance systems, the separation of the view-controller model (the original Smalltalk, though and now almost ubiquitous) and a multitude of posts defined in standard collections and objects.
At the top of my head, Smalltalk is also very different in its flow control system and has a similar, but subtly different, idea of a “block” (although most of the new implementations brought them into line). Apple actually implemented the blocks as an extension at the C level, which is used by many new methods for Objective-C objects.
That being said, the Goldberg Smalltalk-80 book is extremely well written, easy to read, and language so simple that you can learn the whole language in just two or three chapters. Most of the complexity is swallowed by objects available at run time, and it is obvious that the material is not being transferred. The benefit lies in the fact that ideological material about objects and runtime is very much separated from the specifics of printing. Conversely, C does things like flow control and arithmetic, a language function, which means more syntax and more to read before you really feel that you know what is going on.
So, in conclusion: Smalltalk-80 (purple) is definitely noteworthy and extremely useful, but not necessarily completely relevant. Learning C is important anyway; my links to K & R for comparison.