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The main difference between がる and 思う is that がる is used when describing how other people think/feel (or appear to think/feel).
がる cannot be used about the speaker. The point is that you can never know exactly what someone else is actually thinking or feeling, even if it may seem obvious. So in general, 思う is avoided when the speaker is talking about how others think/feel. Instead, がる is used to indicate what the speaker believes they are thinking/feeling, based on appearances.
From the speaker's point of view,
is correct, but
is not correct because the speaker can't be 100% positive that Tom actually wants a new car. Therefore, the speaker uses がる to indicate what appears to be case, i.e. that Tom seems to want a new car. And accordingly...
is the correct way to state this from the speaker's point of view.
I will keep it simple to make it easy to understand. I am sure someone else can provide a more detailed answer.
「XXXがっている」 is used to express that someone currently seems or appears to be XXX, or feels XXX.
「思っている」 means that someone thinks a certain way.
An easy way to distinguish the two is that 「がっている」 is more about observation of one's state of emotion, whereas 「思っている」 presumes how one is thinking. However, this is not an exact distinction and there will be cases where this does not necessarily apply.