In a nutshell, synchronization refers to two or more processes' start and end points, NOT their executions. In this example, Process A's endpoint is synchronized with Process B's start point:
SYNCHRONOUS |--------A--------| |--------B--------|
Asynchronous processes, on the other hand, do not have their start and endpoints synchronized:
ASYNCHRONOUS |--------A--------| |--------B--------|
Where Process A overlaps Process B, they're running concurrently or synchronously (dictionary definition), hence the confusion.
UPDATE: Charles Bretana improved his answer, so this answer is now just a simple (potentially oversimplified) mnemonic.