Is there a difference in meaning between the following two sentences:

1. I just finished reading the newspaper.
2. I have just finished reading the newspaper.

Are all grammatically correct? I have a feeling that sentence 1 is not grammatically correct, though nowadays people don't mind.

Also, what's the technical term of the verb forms above? Let me take a guess: Sentence 2 is called present perfect.
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Comments  (Page 2) 
Dear Mr. Goodman,
I'm afraid you've got a very approximate idea of syntax. Your explanation is totally wrong, even for American native speakers. I just would like to recommend a good book of English Grammar: Practical English Grammar is the textbook I studied on. I cannot show you now all that you are mistaking and your ridiculous oddities, just for instance '... because “finished” is not an ongoing action.' It would take an entire elementary course.
So let me insist: 'Revise Grammar!'
An English teacher
i think you could use both but in two entirely different story:

"you know what happened yesterday? I was reading the newspaper in the bus stop when a car crashed right into a tree nearby."
"so what did you do?"
"I just finished reading the newspaper."
( so he kept on reading after the time of crash until he read enough)

"Hi, what are you up to?"
"I've just finished reading the newspaper and now I'm going to make a cup of tea."
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Which one is correct? I just finished cooking or I have just finished cooking?