I don't know of an official list, but here's come common terms and abbreviations:
L5 - "Light 5," the basic 5-tap combo that all characters have after getting the "Advanced Combo" node in the skill tree
Launch - up-swipe to knock the opponent into the air; difficult/unsafe to land on its own but combos after L5
J3 - "Juggle 3," the basic 1-tap combo that all characters have against freshly-launched opponents after getting the "Advanced Juggle" skill tree node. Unlike L5, the moves in J3 are performed automatically as long as the first one hits, but you can still interrupt the combo with certain Special Moves and Blockbusters.
D - "Dash," forward-swipe to close distance to the opponent; ends in an attack that combos into L5 or the running animation can be canceled early into most other moves
DD - Literally "dash dash," forward-swipe again during a dash attack to perform a move with heavy knockback
S - "Sweep," down-swipe to perform a move with long horizontal reach but is difficult to combo off of since it trips the opponent
B - "Backdash," swipe away from the opponent to create distance
BB - "Blockbuster," powerful equippable moves with a film-strip border that must be charged by hitting the opponent before use. Often called "Supers" in other fighting games. May be referred to as BB1, BB2, or BB3; higher numbers indicate relatively higher amounts of charge needed (they'd be 1-, 2-, and 3-bar moves respectively if we had a more traditional meter system like in SG2E, but in SGM each move's charge is tracked independently). BB3's have skulls in the bottom corners of their border and cannot be blocked or evaded by the opponent.
CA - "Character Ability," a character-specific trait unlocked by the first node in the upper wedge of the skill tree. For example, this is what gives Big Band fighters the ability to take one hit during a dash attack without flinching, lets Black Dahlia fire her grenade launcher, and so on.
SA - "Signature Ability," a fighter-specific trait unlocked and upgraded by most of the nodes in the upper wedge of the skill tree. Sometimes a post will specify SA1 or SA2, referring to the first and second abilities, respectively. For example, Bad Hair Day Filia's SA1 gives her a chance to inflict Bleed on hit, while her SA2 gives her increased Crit Rate against opponents that are Bleeding.
MA - "Marquee Ability," one of two character-specific traits unlocked by completely filling out the skill tree and paying an additional premium of Canopy Coins and Skill Points to unlock; adds a decorative scroll outside the lower half of the character's portrait. For example, Valentine "Combat Clinic" MA gives her a choice between "Trauma Center," giving her allies Final Stand when they survive a big hit, or "ICU," granting Valentine herself Heavy Regen when she suffers a debuff.
PA - "Prestige Ability," a character-specific trait unlocked by sacrificing identical fighters to each other in the Power Up menu. Adds a laurel wreath decoration to the frame of the character portrait that also serves as a charge meter for the ability; tap the portrait to activate the ability for the rest of the fight once charged. For example, Robo-Fortune's "Geiger Counter" PA is charged by gaining buffs and applying debuffs; once activated she immediately gains 5 stacks of Precision and for the rest of the fight she'll have damage reflection based on the number of buffs either fighter has.
Most other acronyms or abbreviated names you'll see are shortened versions of a specific fighter variant's name -- with 210 variants available in-game and (probably) 17 more coming in the 6.0 patch later this month, there's just a few too many to list here.