
purple-stem cliffbrake (Pellaea atropurpurea) and maidenhair spleenwort (Asplenium trichomanes) growing together from a crevice in a wall
It’s been said that botany is the study of terminology. Ferns have a language all their own (mostly). Here’s a little primer on how ferns are structured and described.
A fern consists of a rhizome (a horizontal underground stem), with roots below and fronds above.
The frond is the entire “stem and leaf” arising from the rhizome.
fertile frond of christmas fern (Polystichum acrostichoides)
The frond consists of a stipe, blade, rachis, and pinnae.
The stipe is the portion of the stem from ground level to the lowest pinna (analogous to the petiole of a flowering plant).
the highlighted portion is the stipe
The blade is the portion of the frond carrying the leafy tissue (analogous to the leaf of a flowering plant).
everything except the stipe is the blade
The rachis is the midrib portion of the stem within the blade, and the pinnae (singular pinna) are the green parts of the frond (analogous to the leaflets of a compound leaf).
a single pinna highlighted; the pinnae are attached to the rachis
In twice cut (bipinnate) ferns, the pinnae are further divided into pinnules (sub-leaflets).
a single pinna with pinnules
In thrice cut (tripinnate) ferns, the pinnules are divided into pinnulets (sorry, no pictures!).
There’s terminology for blade shapes, too. An undivided blade is simple.
a frond of walking fern (Asplenium rhizophyllum)
A blade with divisions reaching all the way to the rachis is pinnate (once-cut).

a blade of maidenhair spleenwort (Asplenium trichomanes)
If each pinna is further divided all the way to the midrib, the blade is bi-pinnate.
a blade of marginal wood fern (Dryopteris marginalis)
If each pinnule is further divided all the way, the blade is tri-pinnate (again, no picture).
A blade with divisions not reaching all the way to the rachis is pinnatifid:

a frond of common polypody (Polypodium virginianum)
These terms can exist in combination. This broad beech fern (Phegopteris hexagonoptera) is pinnate-pinnatafid according to one authority,
but it sure looks bi-pinnatafid to me:
Next time, a look at some fertile fronds.