gills, gill slits
鰓 centers on the respiratory organs of fish: the gills and gill slits that allow them to breathe underwater.
鰓 combines 魚 (fish) with 思, which likely contributes the sound. The character was created to specifically denote fish gills.
The left side is a fish 魚, and the right side 思 suggests thinking. Imagine a fish thinking about breathing, and you see its gills moving.
For サイ, picture a sighing fish: sigh -> サイ, as the fish breathes through its gills.
gills; branchia
prosobranchs
external gill
lamellibranches (i.e. bivalves)
opisthobranchs
elasmobranchs
ctenidium; comb gill
sea pen (any coelenterate of the family Pennatulidae or related families); sea feather
Heterobranchia; clade of snails and slugs
pterobranchs (hemichordates of class Pterobranchia)
enteropneusts (hemichordates of class Enteropneusta)
nudibranchs
gill sac; branchial sac; branchial pouch; inner branchial groove; pharyngeal pouch
gill slit
gill lamella; branchial lamella; gill filament
branchial arch; gill arch
gill plate; branchial plate; gill lamella; branchial lamella
gill cover; operculum
gill slit