Not alot of difference between the two semantically. Do you think there is a difference? For me, it is all in the listening.

If two people have different opinions, and they listen and think about each others opinions, even without agreeing, that is a disagreement in my opinion.

If two people have different opinions, and at least one is not really listening or thinking about the other opinion so much as waiting for their chance to continue to impose their own or belittle the other person, that is an argument in my opinion.

Is there a difference in your perception of disagreement versus argument?

An argument is basically ideas and reasoning for or against an idea. Whereas a disagreement is the rejection of such ideas or reasoning.

a disagreement is what a man does
an argument is what a woman does:

not my words but what a friend of mine said

Yes and no. Women tend to act more on emotion than logic, men tend to act more on logic than emotion. That's just in general of course. But, really an argument doesn't necessarily require a disagreement, whereas a disagreement is basically a rejection of an argument.

Just different steps IMHO
A disagreement may or may not lead to an argument.
An argument usually starts out with a disagreement.

I tend to think of "argument" as referring to something active, and "disagreement" as referring to the current status of a situation that has BEEN argued.

However, I am well aware that the term argument in particular, has some specialized applications, particularly in mathematical operations. Both there, and in the disciplines of history, rhetoric, and formal discussion, the term "argument" can refer to the formal statement of a proposal or idea, whether anyone disagrees with it or not.

One popular recent saying related to this, is people who say "Let's not bother to argue, let's just agree to disagree."

It's really the other way around. An argument could really simply be a statement, whereas a disagreement is a rejection of an argument. Pretty much as Igor stated.

Agree.

I know that I can disagree and not be inspired to argue.
I disagree with most of the human race but I don't feel a need to argue many points.
The only time I might argue is when I have a vested interest in the outcome of the argument.

Currently, I disagree with the rent costs of one bedroom apartments.
I argue when my rent is being raised.

I might disagree with a fishing ban at my favorite spot on the beach but it is not so important to me as to argue about it, I just find a new spot to fish. I accept the ban because it isn't that important in the scope of things.

In a relationship, I argue the points that I feel are important enough to argue about. I can disagree without arguing. I can disagree without an indication of my disagreement. I just ignore it.
If something is important to me and will affect the relationship, and I value the relationship, I will make an argument in my favor.
The argument can reveal things about the details that I might not have considered.

There are some things that I can be stubborn about.
Things that really mean a lot to me and hold significance on my quality of life. On those things, I will argue and present my side but I will not tolerate disagreement. I walk away from the relationship.