How does the d.school’s framework for Design Thinking map onto IDEO’s?

Here's how I'm thinking about these DT models.

The Stanford d.school describes the Design Thinking method in (5) steps: Empathize, Define, Ideate, Prototype, and Test. IDEO describes it in (3) modes that are often but not always sequential: Inspiration, Ideation, and Implementation.

I'm assuming that these models describe the same set of activities. For example, user interviews in the initial research phase are part of the d.school's Empathize step and IDEO's "Inspiration" mode.

So here's my question.

What I'm wondering is where the lines are drawn (or if they're inherently blurry). For example, does Prototype map onto Ideation, Implementation, or both? Or is my assumption am I wrong, and these models are orthogonal rather than overlapping? And if so, what is the relationship between them?

Here's what the models look like.

The d.school's model:

d.school Design Thinking steps diagram
(source: kashifzaman.com)

IDEO's model:

IDEO 3 modes diagram