Is there a significant difference between salvation by faith with works and salvation by faith and works? I used to think that sola fide meant salvation by faith irrespective of works. Then I started reading about it and realized it means salvation by faith with works.

Works are necessary for salvation but they do not cause salvation; for faith alone gives life. -- Martin Luther
We are justified by faith alone, but not by a faith that is alone. -- Martin Luther

In my view, its a very subtle and insignificant distinction from salvation by faith and works. Take a look at these pictures:


As far as I can tell, both doctrinal traditions will save the exact same group of people.
Am I correct? Is the difference inconsequential? If so, why is so much effort put forth to distinguish the two?
First a disclaimer, I come from the camp that salvation is by faith alone.  The answer will be coming from my perspective, since the question seems to be geared toward those who hold this view.  It also intentionally goes against the definition of Christianity as accepted for the sake of this community because I think that it's the only way to address the question.  I fully expect opposing answers and down-votes, but I'm also attempting to answer the question to the best of my ability because it's important.

The difference is very important.  It's not inconsequential at all.  

The reason it is important comes down to three things (in addition to what I read in the Scriptures):


Pride
Giving the glory to God, who deserves it.
The command to worship God in spirit and in truth. (Emphasis mine.)



  Ephesians 2:8-9 KJV: For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man
  should boast.


To my view, and those who hold it, if we are attempting to add works to faith, then we are not depending solely on God or the saving grace of Jesus.  We are depending at least somewhat on ourselves.  Since we're told that we are saved by faith along apart from the works of the law (Romans 3:28) if we try to add our own works on top of it, we're not obeying in faith.  

We're placing part of the faith in ourselves, and (this may be harsh) we're calling God a liar by rejecting His clear word on the subject.  In essence, we're worshiping a "god" of our own making - one we've created in our mind, which is, by definition, idolatry.  

This is not to say that works aren't important.  Works are a sign that we have already been saved by faith, and something we do out of gratitude.  I personally would argue that someone who is not showing good works is probably not truly saved because they are not showing the fruit of salvation.  But I wouldn't be dogmatic about it because I don't know the heart or state of salvation of anyone.

There's a good article on the subject here.

I'm adding this later as an illustration that may make the answer of whether it's a "minor detail" more precise.  

Expanding on what I said about taking credit for our own salvation as being pride.  Pride is in and of itself a sin.  God hates pride.

Even a little bit of taking credit for our owns salvation is like having a "little bit" of sin. It's not something that can be seen in shades of gray.  It really is an all-or-nothing black-or-white issue.  Our pastor often uses an illustration in which he holds up a clear glass of water and asks if anyone would object to drinking it.  Then he asks, "OK, let's add just one drop of urine to it.  How many of you would drink it then?"  It's gross, yes. Disgusting.  But that's the point.  God's holiness is so supreme that even the smallest hint of sin is sickening to Him.  Adding the least bit of our own "works" to His gift pollutes the gift.  

In Isaiah 64:6, we read that all of our righteousness is as filthy rags.  Not our sin, our righteousness - the very best we are capable of is worthless to Him.  How could we possibly hope to add to our own salvation when the best we can do is no good at all?