Writing for e-Jewish Philanthropy, Richard Marker makes a solid case against using the terms "non-profit" and "not-for-profit" to describe the sector in question:

After all, if a local boutique loses money, it does not make it a “non-profit.” And conversely, if an organization which is recognized as a US 501C3 by the Internal Revenue Service happens to have an annual surplus, it doesn’t immediately morph into a tax paying “for-profit.” We all know that the bottom line definition has only a little to do with a balance sheet or annual budget...

...The words “non-profit” are suggestive of what a society considers normal. Why call something “non…” if it is the preferred or standard way to do things?... In a very real sense, the words misrepresent the vast scope of this field. In every city, “non-profits” are among the largest employers, the largest landowners, and major contributors to the overall economy...

...There have been no shortage of attempts to more accurately name what this is: “Independent sector”, “third sector,” and “voluntary sector” are two that have resonated with many for a while.

I, though, would like to ascribe to and endorse one of the current formulations which I believe more accurately describe the legal status and gives this essential part of any open society the gravitas it deserves Thus: The distinction should be between two kinds of entities: Those which have historically been called “for profit” are better referred to as “private benefit” entities, and those which have traditionally been called “non-profit” are better referred to as “public benefit” entities...

...Among the benefits of these new formulations is that it would help redress some regrettable baggage which the “non-profit” appellation brings with it. For example, it would remove the association of public benefit organization being viewed only as “charities” existing only for the neediest. That is a worthy and crucial component of the sector, just not the whole thing.

Marker is right that the terms "non-profit" and "not-for-profit" lack substance, defining such organizations solely by what they are not. This problem also applies to "NGO," "Non-Governmental Organization". (If that title were to be taken literally, everything from Coca-Cola to Al Qaeda to a child’s lemonade stand would count as an NGO.)

“Voluntary sector” is misleading because those of us who work in the sector do expect to be paid, thank you very much. “Third sector” is completely vague (one might as well call it Sector 7G) and only marginally less of a negative definition than “non-profit.” “Independent sector” is laughable – no sector is less independent than the sector that sustains itself mostly by asking for money. (Really, no sector at all is "independent." We have an integrated economy.) “Philanthropy” is a venerable word with a noble meaning: love (philos) of humanity (anthropos). But the phrase “philanthropic organization” is quite a mouthful. One can’t refer to an organization as “a philanthropy” any more than one can call a philosopher a philosophy. (The grammatical analog to the philosopher is the philanthropist, but that refers to a person, not a group.) “Philanthropic organization” could be abbreviated as “PO,” but this acronym must be dismissed for other reasons.

So Marker identifies a legitimate need. But really: "public benefit entities?" This proposed term is precise to be sure – precise to a fault. It's cold and technical, devoid of poetry – nearly robotic. Why, I can hardly wait to write a check to a public benefit entity. Then I shall expose animal and vegetable matter to copious heat in order to aid digestion and enhance culinary appreciation during the process of nutritional intake. And on Tu B'Av, I shall write a card for that special someone reading, "This is to inform you that I have a pronounced romantic affinity for you, finding you both sexually and aesthetically appealing. Our overlapping interests and compatible personalities make me confident that we shall remain in monogamous partnership for the foreseeable future. Figuratively yours, [full legal name].”

Is it unrealistic to hope for a revival of the simple word “charity?” Marker notes (accurately, unfortunately) that this word has come to connote helping the needy exclusively, while the field actually encompasses much more than this (the arts, religion, intellectual discourse, etc.). Still, might it not be worth trying to expand the semantic range of “charity” and assert it as a more general term?

This would be a renaissance for the word, not an innovation. Thomas Aquinas defined caritas, from which the English “charity” derives, as “a friendship of man and God” which “extends not merely to the love of God, but also to the love of neighbor.” So defined, “charity” is as broad and beautiful as “philanthropy,” and it’s much easier to say “a charity” than “a philanthropic organization.”

The only objection I can envision is from fire-breathing secularists, but surely even they can find a way to appreciate Aquinas’s definition by taking it figuratively. If they cannot, it will be another symptom of the same affliction Marker’s preferred term suffers, an affliction spreading rapidly in the modern world: a precise term might be something like “pronounced societal metaphor deficiency syndrome,” but I’d rather just say that we could all use a little more poetry in our lives.