Whether a lens is a "fisheye" or "rectilinear" lens is not determined solely on the basis of its focal length. The way a lens is designed also determines the type of projection it makes.
Your 1.8mm lens does have a very short focal length, but is also likely projecting a very small image onto a small sensor area. Such a lens can be made to project a rectilinear image (although it would probably still demonstrate some geometric distortion) or a fisheye image. The difference is in which things are (attempted) to be projected as straight: lines going from the center to the edge of the image like spokes in a wheel or parallel lines within the field of view. Another way of saying it is that fisheye lenses attempt to preserve angles at the expense of straight lines while rectilinear lenses attempt to preserve straight lines at the expense of angles.
There are both fisheye and rectilinear lenses designed for larger sensors (in the APS-C to FF range) that have overlapping focal length ranges. Canon makes a 14mm fisheye as well as a 14mm rectilinear prime. They also make an 8-15mm fisheye zoom lens and an 11-24mm rectilinear zoom lens. All of these are for full frame sized sensors. They also make a couple of rectilinear zoom lenses for APS-C sized sensor that are 10mm on the wide end. Other manufacturers offer similar lenses.
For more, please see these related questions:
Is the focus plane of a fisheye lens inherently curved?
Why don't smartphone cameras correct pincushion distortion automatically?
Does wide angle equivalent in crop sensor skew image?
Why doesn't the GoPro automatically correct for the fisheye distortion?
Why the faces in the corner tends to skew a bit in almost all smartphone cameras