Starting with the more traditional turn based systems and moving on to more 'real-time' systems down the line:
This system has a bunch of cards/spheres/icons in a lineal arrangement which shows turn order. Actions will send your character's icon further back depending on how 'heavy' the attack is.
Other attacks can activate timecards, which are separate instances of activations (such as a healing spell that heals 3 times, once every 10 icons).
Enemy and player actions can be cancelled via breaking - hitting a character long enough can break their icon, making them lose turns until they snap out of it.
Also, certain characters have skills that break the fourth wall and directly interact with the icons, such as Roxis' card management skills in MK1.
Skills also have ranges, but characters and enemies usually can't move, positions are determined on battle start.
Support system from MK1 onwards let you switch the back-row members into the front line, either as attack support (replace the character who just took action by supporting with an attack) or defense support (quickly hit a button before the enemy launches an attack to a character, protecting said character while replacing him or her). This system also allows chaining more and more attacks as long as the back row is able to switch in (or there is enough support gauge points in later titles).
MK games also have a clock system (dungeons go through day and night, but days don't actually go on during them) and it's tied to battles. Each card/icon that passes represents one in-game minute.
Pretty much every Atelier from MK onwards initiate battles via direct contact with an enemy on the field.
Position based - skills can have different ranges of effect (single, small circle, big circle, line, fan spread, whole field), slight real-time aspects when it comes to charging spells. You can cancel enemy attacks just like they can cancel yours. Players and enemies move automatically when using skills or attacks, but there is an evasion option that allows moving a player character.
Each Grandia title has its own spin on how to learn skills, but the way turns work in the games is pretty much the same across the series.
Battles in Grandia games are usually initiated by contact with an enemy in the field.
Turn based, each player or enemy has their own turn, but said turn is in real-time. Each turn is 4-5 seconds long and allows free movement in the field.
Skills are of two types: light and shadow based - they become usable depending on where the user stands. Battlefields have several obstacles which provide shadows or moving objects that do the same (such as clouds).
Game is pretty difficult later on, especially some bosses. Also, the system starts relatively simple but as the story progresses the 'party level' changes, which changes some rules of the battle system and allows new kinds of attacks/supports. NG+ allows the player to set any party level at any time.
Battles are random.
Fully real-time. 3-4 characters on the field at the same time, the player controls only one at a given time but co-op multiplayer is possible (and really damn fun). Combo system present and each title has its own gimmick (elemental rings in Abyss, linking in Xillia, fusing in Zestiria…).
Most titles have battles initiated by contact with enemies, but there are exceptions which use random battles instead.
Definitely gets intense, especially on harder difficulties (changeable at any time outside battles). Definitely recommended to try out co-op.
Also for what it's worth, the upcoming FF7 remake seems to have a KH-like system.