“Unconventional” versus “new”

Unconventional

Means:

unusual relative to the dominant or established approach.

Example:

Historians normally explain industrialization through technology, capital, and markets. A historian emphasizes legal status instead.

That could be unconventional.

New

Means:

not previously proposed or developed in that form.

A genuinely new argument could also be conventional in the sense that it fits the field's existing approach.

How can they overlap?

Suppose everyone studies industrialization economically, and you introduce an entirely new legal explanation.

It is:

• new because nobody previously proposed it;
• unconventional because it departs from the dominant approach.

But:

An old idea rediscovered in a new field

could be unconventional there without being genuinely new.