What is the word for something that is based on a prototype?

Depending on context, you could call a non-prototype a production model, although it seems that this term refers primarily to vehicles. You might also replace model with unit or version. This Google ngram seems to indicate that production unit is the most popular of those three options.

If you are dealing with software, you could call it shipping a 1.0 product or merely a 1.0. Release version is another candidate. And if there are multiple prototypes, they are sometimes referred to as pre-alphas, alphas or betas in the programming community. A prototype that is almost ready for distribution is often called a release candidate.

Added: see this related question dealing with the opposite of a proof of concept.

While I like longstreth's production unit, you also might consider finished product

the product that emerges at the end of a manufacturing process

SUPPLEMENT:

I think part of the problem is the term prototype. This is often used in the sense of

a first, typical or preliminary model of something, especially a machine, from which other forms are developed or copied

While it can also be understood as archetype it often conveys preliminary.

You may want to consider the term derivative

something that is based on another source: a derivative of the system was chosen for the Marine Corps' V-22 tilt rotor aircraft

It can be used as a noun on its own or as an adjective with version, model or other noun. It is the term used in copyright law (which covers a good deal of programming) in the phrase derivative work which refers to a creative effort that is based in substantial part on a prior work.

In a more figurative vein, you could use the term daughter.

•(literary) a thing personified as a daughter in relation to its origin or source: Italian, the eldest daughter of ancient Latin

•(Physics) a nuclide formed by the radioactive decay of another.

Continuing the familial theme, patent applications are often referred to as parent and daughter applications, the latter following, being based on, and often refining the concepts contained in the former. The junior patents are also called child patents.

Derivative can be used as a noun or as and adjective (as in "derivative design"). Another noun is derivation.

A derivative is something derived.

Derive is to take, receive, or obtain, especially from a specified source; to have or take origin.

Derivation is something derived; or an act or process of deriving.

To modify your original statement

This will not be true for versions that are based on this version.

you might say

This will not be true for derivatives (of this version).

or

This will not be true for derivative versions (of this design).

where the parenthetical can be left implicit if you like.

While it might sufficiently explained, let me provide some examples of it's direct and related uses:

Derivative Design - new designs that are based upon existing designs, using design elements, concepts, or principles taken from those existing designs.

Derivative Product:

New product that results from modifying an existing product, and which has different properties than those of the product it is derived from.

Also, under U.S. copyright law:

A derivative work is a new, original product that includes aspects of a preexisting, already copyrighted work.

As with many words, "derivative" has other meanings besides this one, but this should not be a limitation when used in the right context.