I don't think 'without' or 'outside' groups mean the same as 'between' groups (and similarly for 'inside' and 'within').
Let me try to explain my point by using these words in a context of comparison. Let's imagine once each student has given her or his weight the teacher ask the students the following questions:
1) What are the difference of weight BETWEEN male and female students? 2) What are the difference of weight WITHIN male students? 3) What are the difference of weight WITHIN female students?
First let's imagine how the students could have answered. For question 1 a possible basic answer would be to calculate the mean weight of male students (let's imagine it is 70 kg) and then the mean weigth of female students (let's imagine it is 60 kg). The obsious conclusion (however possibly statistically incorrect) would be that boys are heavier than girls by a difference of 10 kg. For question 2 a possible answer would be to calculate the difference between the heaviest boy and the lightest boy. For question 3 a similar answer could be given for girls.
We have just imagined an example of comparison where 'between' and 'within' have precise meanings which can be understood by answering math questions. Now if you do not see the difference with 'inside' and 'ouside' let's use these words in the previous questions:
1) What are the difference of weight OUTSIDE (or WITHOUT) male and female students? 2) What are the difference of weight INSIDE male students? 3) What are the difference of weight INSIDE female students?
First you could say that the use of 'inside' in place of 'within' is not that much of a shock in question 2 and 3. However a possible interpretation would be to search for weight differences inside the body of each student which does not make any sense. Second please read question 1 out loud. To me it does not make any sense and it is the strongest evidence that 'outside' or 'without' cannot replace 'between'. And to me the same applies to 'inside' and 'within' even if it is less obvious.
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