The difference between Heterogeneous and Manifold

Heterogeneous as an adjective:

Diverse in kind or nature; composed of diverse parts.

Heterogeneous as an adjective (mathematics):

Incommensurable because of different kinds.

Heterogeneous as an adjective (physics, chemistry):

Having more than one phase (solid, liquid, gas) present in a system or process.

Heterogeneous as an adjective (chemistry):

Visibly consisting of different components.

Heterogeneous as an adjective (computing):

Of a network comprising different types of computers, potentially with vastly differing memory sizes, processing power and even basic underlying architecture; alternatively, of a data resource with multiple types of formats.

Manifold as a noun (now historical):

A copy made by the manifold writing process.

Manifold as a noun (mechanics):

A pipe fitting or similar device that connects multiple inputs or outputs.

Manifold as a noun (US, regional, in the plural):

The third stomach of a ruminant animal, an omasum.

Manifold as a noun (mathematics):

A topological space that looks locally like the "ordinary" Euclidean space \mathbb{R}^n and is Hausdorff.

Manifold as a noun (computer graphics):

A polygon mesh representing the continuous, closed surface of a solid object

Manifold as an adjective:

Various in kind or quality; diverse.

Manifold as an adjective:

Many in number, numerous; multiple, multiplied.

Manifold as an adjective:

Complicated.

Manifold as an adjective:

Exhibited at diverse times or in various ways.

Manifold as an adverb:

Many times; repeatedly.

Manifold as a verb (transitive):

To make manifold; multiply.

Manifold as a verb (transitive, printing):

To multiply or reproduce impressions of by a single operation.