Some asshole downvoted you, so I gave you an upvote because there's nothing wrong with admitting you don't know something. Welcome to today's 10 000! ^_^

As for your question, a nonprofit cannot make profit and has to work toward a societal good, while a not-for-profit also cannot make profit but is not bound to that obligation.

From this article:

While all types of nonprofit organizations share the common goal of not pursuing profits, their legal and operational characteristics can differ:

Mission: Nonprofit organizations are required to benefit the public or advance a social cause. Not-for-profit organizations, or “other nonprofits” as the IRS deems them, can also benefit the public or they may focus solely on benefiting their members.

Scale: Nonprofits are typically larger organizations that aim to fulfill a larger need, such as the American Red Cross, while not-for-profits (or “other nonprofits”) are often smaller, serving only their members, such as a social club.\

Revenue Sources: The revenue of a nonprofit organization primarily comes from donations, grants and memberships. The revenue of a not-for-profit organization (e.g., a social welfare organization, civic league, social club, labor organization, veterans’ club or business league) is mostly derived from sales and membership dues.\

Tax-Exempt Status: Nonprofits are often granted tax-exempt status under section 501(c)(3), while not-for-profits (or “other nonprofits” as the IRS calls them) can be tax-exempt under other 501(c) sections.

This is, perhaps to needless to say, a US-specific distinction and may be different or even nonexistent in other countries. :)

Cheers! <3