GHEIST focus on damage and poison while Roots focus on life gain and damage reduction.
Fang Pi Clang is about SoA-resistant high-power cards compared to La Junta's current shaky support (I feel they need some help right now). This pairing has identity issues. I'm hoping La Junta get more pill cards to help push the two further apart.
Bangers are damage-centered with light pillz effects while Ulu Watu have higher power and life gain with little damage.
Piranas control the pillz and Nightmare scares your opponent with damage, life gain/drain, and poison.
Junkz are evenly spread in EVERYTHING except damage. Sentinel are also evenly spread, but don't touch pillz.
Uppers are 2HKO-focused, Sakrohm is about defense with higher power, and Montana is somewhere between them, but with an awkward bonus minimum.

Roots has more base power but less base damage
junta and fang pi differ mainly in abilities
Bangers have less base power then Ulu Watu but Bangers also have better abilities
Piranas have the higher base power but can lack in the life gap
Junkz have more base power but sents support eachother better
Uppers has the strongest attack to minimum ratio or in other words have the low pill advantage, Sakrohm has lots of great abilities at their disposal, Montana have the better high pill advantage

this is all my opinion from what i've seen and my off the top memory of the clans, opinions may differ.

Roots = more atk manip and DR based
GHEIST = power manip and damage

Piranas = solid all around w/ a bit of everything but their main focus is pill manip
Nightmare = weaker general winning power (too many 5-6 power) and few have abilities that help win rounds but high threat power (Kenny Cr & Cutey = huge life gap, Azel & Karrion huge deadly round 1 poison, Kolos, etc.)

A few of the most noticeable differences I've seen:

Roots might have the most solid set of 3* in the game – Noodile Cr, Rico, Gertjan, Jeena and Yookie specifically. Nothing too spectacular, but facing any combination of those five can prove to be really difficult in ELO.

GHEIST rely on heavy damage and are more dependent on their SOA bonus to win the match. As a result, I feel like they usually have more trouble against Skeelz and SOB clans than Roots do.

Bangers have rather poor base stats but the highest average base damage in all of UR. As a result, 2HKOs become a regular strategy.

Ulu Watu, on the other hand, generally have extremely high power and will win most battles with five pillz or more. They have lots of +life abilites and are generally on the more defensive side.

Piranas win by stealing your pillz primarily. However, they often need to win three or more rounds in order to win the match. Winning with Hawkins, Puff and Sting isn't enough if the opponent has a fully supported Avola waiting at the end.

Nightmare have a bunch of really powerful, and frankly, really scary abilities to play around with. These scare tactics are usually important to win the game. How the hell do you distribute your pillz if you're facing Cutey, Sheitane, Kenny Cr and Karrion?

Out of the attack manip. clans, I feel like Sakrohm stand out the most. These guys usually rely on unbeatable life gaps with lots of really powerful damage reduction and +life abilities.

The biggest difference between Junta and Fang Pi Clang is play style. Junta focus on threatening to KO you. FPC focus on utility and flexibility; they can focus on KO or denying gap. Cards like Chan, Fei, Futoshi Ld, Shifou, Heitachi, Nakata, and so on, are all designed to be able to beat certain kinds of high-threat cards.

Junkz - Sentinels

Junkz has random assortment of pretty much everything with moderate twist to pill manipulation while Sentinels is all about good/great power and extremely useful attack manipulation and other abilities are very minimal. Also Sentinels have good selection of staple support-type cards making sentinels most serious when used mono, while Junkz go well to halfdecks.

For me, the difference of those clans i think is their mind set in battle

Sentinel - will K.O. you
Junkz - will get your pillz and force a 4 round battle

G.E.I.S.T. - will K.O you
Roots - will gain life in front of you

Bangers - will K.O. you
Ulu Watu - will gain life in front of you and K.O you eventually

La Junta - will deceive you and when they have a chance, they will K.O. you
Fang Pi Clang - will threaten you and gain life but will K.O. you anyways
(btw, the Berzerk clan can be also similar in FPC and juntas, they have +2 dmg, but the Berzerk remove it and has limit
for the sake of being similar here's their mind set
Berzerk - will K.O. you at later rounds)

Piranas - will take your pillz and K.O you.
Nightmare - will scare you to death and suck life which will lead into a K.O.

Uppers - will K.O you while laughing their ass off because you can't reach them
Montana - will K.O you
Sakrom - will heal in front of you and will laugh at your 1 dmg..