Making sense of 다르다
옛날 과 달랐어요.
What is this grammar? Can someone please explain this?
How does this possibly mean 'it's different from before'?

EDIT: I have no trouble understanding the past tense conjugation of 다르다, it's the 옛날 that I don't.
I thought A+와/과+B = A is B.
If that's the case then this sentence says 'before is different'

Actually, you know what. It's saying 'before WAS different' right? Is it a natural sentence construction?

EDIT:
Could I then say '저 여자 옛날 과 달랐어요' to mean 'that woman was different before'? and other sentence constructions used similarly?

Question

Making sense of 다르다
옛날 과 달랐어요.
What is this grammar? Can someone please explain this? 
How does this possibly mean 'it's different from before'?

EDIT: I have no trouble understanding the past tense conjugation of 다르다, it's the 옛날 that I don't. 
I thought A+와/과+B =  A is B. 
If that's the case then this sentence says 'before is different'

Actually, you know what. It's saying 'before WAS different' right? Is it a natural sentence construction?

EDIT:
Could I then say '저 여자 옛날 과 달랐어요' to mean 'that woman was different before'? and other sentence constructions used similarly?

Answer

~와/과 means 'together with'.
For instance,
오늘은 어제와 다르는 것 같아요 (today seems different (together) with yesterday)
A와 B (A and B, A together with B)
Therefore 옛날과 달랐어요 means 'it was different with before (old days)'
The subject was omitted, the full sentence could be :
그땐 옛날과 달랐어요 (At this time it was different with the old days)
But it depends on the context you've read this phrase.

파이팅!

Answer

(조건을 비교했을 때 그것은) 옛날과 다르다.
It's different (from the past considering the condition).

Actually it's not '-와/과'and, but the abbreviated type of '-과는/와는'compared to something

그때의 나는 멍청했지. 그러나 지금의 나는 그때와(는) 달라!
Yes, what I was is silly. but what I am is different compared to something!

Answer

1. yes, but stick to 옛날 and 과. 옛날과는

2. it's not necessary but if u feel it's needed it's okay to add something.