Fins on fish help them swim.
Fins usually have bones and skin like a webbed appendage, or like a paper fan that can open and close.
Finlets are small fins. Finlets do not retract (close).
Not all fish have finlets.
There are six types of fins: (1) two pectoral fins, (2) two pelvic fins, (3) a dorsal (back) fin, (4) an adipose fin, (5) an anal (bottom) fin, and (6) a caudal (tail) fin.

fin diagram, Lampanyctodes hectoris by Lukas3, Wikepedia, 17 July 2006
Fins retract (open and close), but finlets do not retract. Finlets are hard ‘stumps’ that do not move.
For example, salmon have an adipose fin between their dorsal and caudal fins. Tuna do not have an adipose fin. Instead, tuna have two dorsal fins and a few finlets.

finlet diagram, Thunnus obesus (Bigeye tuna) by Dr Tony Ayling, Wikepedia, 14 May 2006
Note:
‘let’ means small, young, or baby. A finlet is a small fin. A piglet is a baby pig. A froglet is a baby frog. A toadlet is a young toad. A snakelet is a young snake. But a hamlet is not a small ham (a hamlet is a small village or town).
Photographer: Martina Nicolls
Martina Nicolls: SIMILAR BUT DIFFERENT IN THE ANIMAL KINGDOM