Broadly speaking, they're just a different way of saying the same thing. The following examples all mean the same:
1. 我学了一年 的 中文
2. 我学了一年 中文
3. 我学中文一年了
Notes:
a - A slight difference among them is example 1 is a bit more formal than 2 and 3.
b - In some contexts, the meaning of 3 can be slightly different from 1 and 2
Sorry, I can't agree with you.
As SuperXW said, the school grammar, which is based on the 暂拟汉语教学语法系统 designed 50 years ago, has a different analysis than I.
Despite the differences in grammar structure, their meanings are also different.
1)
You can say “我(先)学了一年中文，然后……” and “我(先)学了一年的中文，然后……”
But you can never say “我学中文一年了，然后……”
You use the 了 in the first sentence to report "something happened".
And you use the 了 in the second sentence to report your cognition (about the current state).
2)
You can say “我学了一年(的)中文，然后……”
But you can't say “我学了中文一年，然后”
You can say “我爱/骗了他一年，然后” and “他爱/骗了我一年，然后”
But you can't say “我爱/骗了一年(的)他，然后” “他爱/骗了一年(的)我，然后”
I don't know how to determine which form should be used.
It seems that when the object is a person/people, you can't put a 数量词 before it. (an exception: put the 数量词 before the object if the 数量词 and the object refer to the same thing. e.g. 杀了三个人)
The verb is also important.
Both are acceptable:
他去/待了五年(的)上海，然后
他去/待了上海五年，然后
When the verb means “to do work that you can initiatively decide how much to do”, you will usually put the 数量词 before the objective.
It seems that the position of the 数量词 varies with that of the 了:
他缺席了三天，然后……
他缺了三天席，然后……
3)
verb + Time duration + 的 + object
does not need to mean
verb + Time duration + object
e.g.
他做了一天的工作。 cf. 他做了一天工作。(how much to do)
他结束了一天的工作。(NOT how much to end)
他开始了一天的工作。(NOT how much to start)
