Yes, you can in the same round, but not the same turn.
Let me explain. You seem to be using different terms interchangeably when you shouldn't.
You get in a round exactly ONE TURN (baring certain weird PrCs)
In a turn you get:
Unlimited Free Actions (Technically. The DM is allowed to put limits) But we don't care about free actions for this discussion. They exist, it's all that matters.
The base three actions:
1 Move Action
1 Standard Action
1 Swift Action
There are also two different actions that are modifications of the base three:
The Full-Round Action
The Immediate Action
A move action will always be a move action.
A standard action can be a standard action or a move action.
A Move and Standard action can be combined to make a full-round action.
A swift action can be a swift action, but it can also be an immediate action.
The immediate action can take place at any time, but it uses up your NEXT swift action in your NEXT turn (even if you are currently IN that next turn.). It can interrupt any action, another PC's action, an NPC's, or even YOUR OWN actions. For example:
A. I am in a fight. I use a quickened magic missile. It uses up my swift action. I jump off a cliff. Falling is a free action, I hit the ground. I would love to use feather fall as an immediate action, but I can't. Falling is a free action and it resolves first. I have no swift action left, because it is still my turn.
B. I am in a fight. I use a quickened magic missile. It uses up my swift action. I instead flip off the Dungeoncrasher as a free action and end my turn. The very next initiative count, the Dungeoncrasher Bull Rushes me and pushes me right off the cliff. Falling is a free action, BUT I choose to interrupt my own fall and cast feather fall, an immediate spell. It uses up my NEXT swift action.
Upon hitting the ground I stand there and wait. The round ends, a new round begins. My turn starts again. I get a Move action, a Standard action, but I already used my Swift action. I cannot activate any swift action items. I cannot perform any swift action feats. I cannot cast a quicken spell. However, the moment I am willing to say, MY TURN IS OVER, I can cast an immediate spell.
Do not confuse turns, rounds, and full-round actions.
A turn is what happens when my Initiative count is reached:
Ed goes on 5
Mark goes on 3
NPC WARGO the BURNIATOR goes on -2
Doesn't matter. You could have a -45 to initiative, but everyone gets 1 TURN every ROUND. Initiative isn't a matter of how fast you go, just the order.
A round is a unit of time. If I cast a spell that takes 1 full-round ACTION to cast, then I get to do it ON MY TURN, but it still happens on my turn WITHIN a round.
If I have a spell with a 1 round casting time, I start casting on my turn and DO NOTHING. I can't take a swift action. I can't have used an immediate action before this turn. I must have my full turn at my disposal when I start to cast my spell with a 1 round casting time. THEN, I declare I am casting the 1 round spell and my turn ENDS. I do NOTHING until my next turn. During that whole time I am casting, I am subject to AoOs to anyone who wanders past me, subject to interruption, there are so many ways to mess with me because I can't even take a 5 foot step.
At the start of my next round, The spell goes off, and I get a turn with all my actions refreshed. But during that round, I can't do jack, can't even use an immediate action because it takes the WHOLE round, not the FULL round.
In effect, during a 1 round casting time, my turn never ends. My turn is on going and I am frozen, gesturing, murmuring, whatever, until the spell resolves.
You can then extrapolate that out with 1 minute, 10 minute, casting times. Or 10 round and 100 round casting times.
Sounds like you are confused about what a full-round ACTION is and what a 1 round casting time is. They are NOT the same.
And note, it was even more confusing in 3.0, where it wasn't a full-round action, it was just called full-round. People got confused about full-round meaning 1 round. Because, hey, 1 round is a full round, right? They added full-Round ACTION to make it stand out more, but really, someone at D&D needed to get a thesaurus.