Although it's confusing because literature and the media often use FinFet to mean any non-planar device, and frequently use the terms interchangeably, the original FinFET design from UC Berkeley is a non-planar ("3D") dual-gate transistor. Intel's tri-gate design is a non-planar tri-gate transistor.
The paper that I consider to be the one that named the "finFET" is this one:
"Sub-50nm P-channel FinFET" Quejue Huang et.al, IEEE Transactions on Electron Devices, Vol. 48, No.5, May 2001.
In the abstract: "High-performance PMOSFETs with sub-50-nm gate length are reported. A self-aligned double-gate MOSFET structure (FinFET) is used to suppress the short-channel effects."
If you Google it, you can read the paper. Like I said, I find it confusing too - first because a finFET looks like a tri-gate when you look at the electron microscope photos, and second because people seem to use the term "finFET" to mean any non-planar multigate transistor. To me, when I hear the term "finFET" I think of the paper from 10 years ago and then the subsequent dual-gate papers from TSMC and this is a distinctly different design from Intel's tri-gate.
* Not a spokesperson for Intel Corp. *