Concepts: Core, Processor, CPU, Die, Package, and Logical Core

Definitions
Cores are just core units, meaning the basic compute unit inside the CPU. A core may also have its own caches.  One core, one thread.  
A die is a continuous piece of semiconductor material, like a square.  There can be many cores on a die. 
A processor package can have multiple CPU dies. 
The term “CPU” is ambiguous.  Strictly speaking, a CPU is a processor.  But people use it in a more general sense. "When people buy "a CPU, they buy a CPU package. “ Sometimes a CPU means a core inside a processor, because multi-core processors act like they have multiple CPU in it.  

Logical Cores:  Each logic core can execute one thread. But multiple logical cores are still based on one physical core. We can do that because hyper-threading. 

Quantitative relationships between these terms
Processor package 1—* dies
Processor 1—1 die
Processor 1—* core
Core 1—1 thread

Note: 1—* means one-to-many.  1—1 means one-to-one

From software developers’ view 
Quote from [2]:  "From a software point of view CPU or cores are seem pretty much the same, it doesn't know if they are each on its own die, or are etched on the same die. They are treated as independent processing units, so you can run different tasks on each of then.”  

References 
1.  The third answer in http://stackoverflow.com/questions/19225859/difference-between-core-and-processor  
2.  http://superuser.com/questions/324284/what-is-meant-by-the-terms-cpu-core-die-and-package