What’s the difference of powers/constructs for the emotional spectrum lanterns

The rules are pretty fast and loose but

Green: you can make a construct of anything if you have enough willpower and understanding/imagination. Also translates alien languages, flight in space including faster than light, both of these are pretty universal with rings. Depending on situation can’t affect anything yellow, has a charge limit tha needs recharging, constructs can fail if concentration lost.

Yellow: similar to the above almost exactly, but can be fueled or strengthened to some degree by creating fear in people nearby. Only usable by people who understand fear and instill it in others to a great degree.

Red: Originally those with Red rings couldn’t make constructs due to lack of focus. Powered by rage about tragedy, rings generallly replace users hearts and transform blood in red plasma like stuff that burns everything, can eat through constructs. 

Blue: has basic abilities in addition the healing abilities (whether reversing supernova’s or regenerating people’s limbs). Constructs and some abilities only usable when around Green Lantern rings. Rings were designed to be symbiotic with GL rings so they super charge GL rings, can heal and safely remove red rings, and reduce power in yellow rings. Powered by hope, which apparently without willpower is week

Orange: pretty similar to generic ring with a few caveats. Ring makes user overcome with greed since that’s what powers it. People killed by orange ring are then recreated as constructs for orange lanterns.

Indigo: rings force user to feel compassion, and since most users are sociopaths, also channels other rings abilities to make them feel other emotions as rehabilitation (or brainwashing depending on who you ask). Also capable of instant teleportation.

Violet: similar to GL ring but powered by love. As such a couple weird abilities like brainwashing people by manipulating their love, as well as teleporting lovers to each other or healing one lover with another’s life force.

Black: Zombies whose rings suck up light/emotion from other rings or people’s hearts. Destroyed by lights combining to make white light. Generate black goo constructs to make people more emotional.

Again, all of this is pretty fast and loose, and is mostly around to look cool.

Never read any of the comics but in GLTAS there seems to be different trends in what constructs/‘element’ each corp makes.

Green Lantern’s constructs are like energy holograms. Blue Lantern’s are like light energy. Red Lantern’s constructs have a flame burn feel to them as well as being sharper. Star sapphires’ constructs are crystallized and orange lantern constructs have an electric aura around them. I think these little differences adds a lot of character to each corp. Crime the show was cancelled

(Also it seems like in the series the Green Lanterns make the most diverse constructs, maybe they are more creative or show just maxed its budget lol)

I would say that the entire concept is somewhat in flux. Sinestro's original "yellow ring" originally came about as the "ultimate threat" against Hal Jordan because his ring still had the yellow vulnerability; once Hal became (infected by) Parallax and eliminated the vulnerability, the GLs now had no unifying weakness; failures of imagination on each Lantern's part became something the writers had to create one by one.

Across all the Corps, adding a new, fundamental weakness to each one of the emotions needs to get decided at the editorial level so it can stay consistent... At least until the next editorial shake-up happens.