Try clearing the site data (clear cookies and history) or use hard refresh (F5) when you load the site. In incognito mode, the scripts and sheets are loaded freshly whereas in normal mode, the browser stores your files in cache memory in order to lessen the wait time. I hope this answers your query
So, you are using the same browser on the same computer to perform the two tests, yet, in the incognito mode it works correctly, while in normal mode the slider does not work. You did not specify how it is not working, but from a more abstract perspective it does not matter, I presume. Instead of focusing on your actual slider, I will focus on the more abstract:
My page works in incognito, but not in normal mode
There could be many possible cases, you might be affected by one or more from the possible problems described below.
It is possible that you are simply not loading the page in the same way (the protocol, the get parameters or even the path may differ).
In order to make sure you do not have this problem, simply copy and paste both URLs into a text editor and see whether there are any differences.
Your client-side files, such as JS/CSS files are being cached by the browser and will not change upon each reload. You will need to empty your browser cache in normal mode.
You may be already logged in in normal mode with a user, but the login might have happened before some changes were made on session initialization logic and you remain with the undefined behavior.
Log out and log back in.
Compare the values of localStorage in normal mode with the one in incognito mode and do the same with sessionStorage. If you see differences, then you might have found the culprit.
It is important to perform the test the same way on the two different use-cases. To be logged in with the same user and to use the same page the same way. So, session/page differences will not confuse you.