First off, it sounds like what you have is two inexpensive windows. The second (or inside) one was installed to soundproof the first. Question one: are they effective against the noise from the busy street?
What you have is not so unique. You will probably need to remove both windows and install a new window (I would recommend a casement type) with sound glass in a "new construction" method. Why I asked about the effectiveness of your current windows against sound is that a window is only part of the entire sound equation but that is a completely new discussion.Good luck!

It does a pretty good job at blocking out the sound when both are closed. It's just nearly impossible to open and close the outside window properly without feel like I'm about to push the window way from the house. Doing this over the years has damaged the frame around the glass and the outside track.
I was told perhaps keep the existing inside window and take out the outside one and replace it with a storm window but I don't know what that is or what it does.

Your weird window happens to be quite common in the Northeast. The outside one is the original and inside storm was installed later because the oem window was a builders special. Just like having basic coverage in an auto policy just to have insurance.
The remedy is simple. Get rid of them both and replace it
with a real window.

Any window professional will know what to do.
As far as what to replace it with, your choices are numerous.

All the best,

The Porch Guy

Here is a link that might be useful: my album