Territory on a Chessboard

I was teaching the subject of space in chess, and my student asked me an interesting question that I didn't have a good answer to: Is space determined by the number of advanced pawns you have or by how much farther advanced a single pawn is?  For example, take a look at the two diagrams below.  In which position does white have more space and why?  What would be a good way for me to explain this concept to a beginner?

In general, space is really about how many squares you exert control over.

Though with respect to pawn chains, I look at it as how much room your pieces "behind" the forward-moving pawn chains have to maneuver around.

Think of it as being the ceiling of a box-shaped birdcage and watching it rise up or go down depending on how the position changes. Assuming you have birdies inside that want to move around and play, a higher ceiling means more room to fly around and get from one side to the other quickly.  

Now the concept of a space advantage refers to the fact that you're evidently "creating" a lower ceiling for your opponent's birdcage (by making yours higher!)  ... and therefore making his pieces suffocate/tying them down.

On the flipside, grabbing space can often mean overextending your pawns and making them targets for your opponent to go after.

Thanks for your help.  I guess the answer is that you have to weigh how much both moves actually restrict the opponents pieces.  The d5 pawn is overextended, whereas c4 controls more squares without undue risk.  

Keep in mind that in terms of strategic concepts, Space is typically the "hardest" to incorporate in one's own games "accurately" for beginners.  Ideas like Knight outposts, open file + rook penetrations and color complexes are relatively simpler to "see in action" in one's own games.