in short the architecture identifies the major components (and their interaction) of a whole software system on high level. Usually an architecture description doesn't care about details in the code. In your example for a 3-tiered application the three layers could be identified as architecture components at the highest level. Additionally you could break up each layer into more components for a fine-grained view on the software.
A design pattern in contrast is something completely different. Design patterns are some sort of recipe to solve common software problems. Design pattern are developed for similar coding problems which repeatedly occur in software systems. So design pattern come into play at a very low level of an application.
Of course this description is very oversimplified but you'll find lots of information on this in the internet or books on these topics.