Purely Turn-Based
Typically in these games, players take turns passing all of the mechanics or opportunities to interact back and forth. When it's not your turn, you essentially can't play. You can hope for the best. You can observe your opponent's moves. But you have to wait until it's your turn to do something about it.
Simultaneous Turns
In these games all players take their turns at the same time in double blind fashion and then watch the action play out. With single player games like Shiren or RO9, if the player acts quickly the gameplay can seem to flow smoothly as if in real time. Games like Floatilla and Pokemon are still turn-based because the gamestate waits for both players to make a move.
Turn-Based with Interrupts (micro turns)
These two card games are turn-based like Poker, but they also have mechanics that players can use when it's not their turn. Thus a micro turn can be defined as a turn with comparatively limited mechanics or options that are only available when the main turn is passed to another player (ie. when it's not your turn). Because micro turns are still turns, they can also hold up the progress of a game until the player makes a choice one way or another.
Turn-based gameplay is great for for simplifying and focusing gameplay. Without any real time elements reflex, dexterity, and timing skills are minimally stressed. This leaves only knowledge and adaptation skills. Because the gameplay waits for player actions, players can slow the pace of a game to a more comfortable level. Furthermore, since time and actions are organized by turns, strategies can be made by considering the interplay possibilities per turn. Understanding the limitations of one's actions based on the limitations of each turn is a critical first step in the strategic process.
With that said, there are many turn based games that have real time mechanics and challenges. Here is where the lines between real time and turn-based gameplay begin to blur. The most basic example is...
Turn based with a Time Limit
Formula: take any purely turn-based game and limit the player to completing their turn within a time limit. The timer is a real time element that creates tension. Though the game actions may not continue until you act, by the end of a timer your "end turn" action will be forced. This fits with the definitions we established.
Real-turn based
Perhaps micro turns or interrupting mechanics are most clear in a game like Mario & Luigi 3: Bowser's Inside Story. When it's your turn, you can attack, use items, etc. But when it's the enemy's turn to attack, you have access to an entirely different set of mechanics. When on the defensive, you can either JUMP or HAMMER to defend yourself. Additionally, though the gamestate holds on your turn until you make your choices (turn-based), the challenges are real time challenges stressing all of the DKART skills. Timing button presses for the basic attacks or using the touch screen controls for special attacks are all real time action challenges. In other words, the turn-based design controls the real time gameplay.
Playing RPS in real life is a turn-based game executed in real time. Ideally, both players try to throw their hand at the same time to prevent either player from using their reflexes to gain an advantage. If you throw your hand too early, that's your fault. If you throw your hand too late, you'll be penalized. So, the game doesn't start until both players are ready, but once the game is prepped, there's no turning back.
The Earthbound battle system is turn-based like Pokemon. An interesting feature to this game is that powerful hits drain your character's hit points slowly. If you suffer a killing blow, by rushing through your turn, you may be able to heal injured character before they die.
In some Boom Blox multiplayer modes, players take turns throwing objects at block structures in attempt to knock off pieces to earn points. While the throwing is turn-based the structures all bend, sway, and topple in real time. On your turn, if you wait too long, the structure can fall giving points to the previous thrower. If you quickly throw on your turn, you can "steal" the points. But if the next player act swiftly as well, they can reap all.
Real Time or Turn-Based
Some games let the player control the way time plays out. In Fallout 3 players can fight in a post-apocalyptic world in real time like an FPS or turn-based style using the V.A.T. system. With V.A.T.S. the action is paused and players can select specific targets and limbs to attack.
The Final Fantasy series (past IV) and Chrono Trigger have ATB (active time battles). Before, players would select commands for all of their characters to play out simultaneous against the enemy's attacks. Dragon Quest still uses this battle system. But with ATB, each character (and enemy presumably) has a meter that indicates when their next command opportunity will come up. This allows some characters to be faster than others and gives the battle a real time design. More importantly, these games have "active" and "wait" options. In wait, while players are selecting commands in the menu, the battle actions stop. In active, enemies and allies will continue attacking while you're in menus. So you can essentially pick a turn-based experience or a real time one.
To close, I must bring attention to a bit of vague language. We commonly use the word "turn" or "phase" to describe when the player has an opportunity to do any action whether in a limited/rare/timed situation or not. For clarity, I'll use "opportunity," "chance," or "moment" for this more general idea, and "turn" only to refer to situations where the game waits on player input.
I've presented a lot here. If you have more examples to add, then feel free to do so. KirbyKid ends his turn.