Mac running slow and some applications don't open in standard mode, but in safe mode it works well
One place to start is testing your Startup/Login items, as it's likely to be something that's getting loaded during normal startup (e.g. a Startup/Login item, a font you've installed, etc) that's causing the problem. 

So I would:


Startup normally
Go to System Preferences > Users &amp; Groups
Select the Login Items tab
Take a note of your Login Items 
Now remove all of them by highlighting them and clicking on the - button below
Restart your computer


Now your Mac will boot up without those login items loading. Test this and see if the problem persists. 


If the problem does persist, I'd then remove any fonts you've installed yourself.
If the problem goes away you know one (or more) of the Login items were causing the problem. You can then go back and add them back one by one until you've identified the culprit.


Let me know how you go.

[EDIT]

I forgot to answer your question about what the difference is between booting into Safe Mode and booting normally. In a nutshell, booting into Safe Mode:


doesn't load Login Items and any custom fonts you've installed (which is what my answer above is based on)
ensures that only macOS kernel extensions are loaded
runs a number of additional checks during startup (e.g. verifying/repairing your drive's directory, etc)
deletes various caches


The last two can result in your system effectively repairing itself if your problems are related to corrupted caches or directory issues. In your case, since the problems didn't go away after previously booting into Safe Mode, the problem is most likely related to Login Items or 3rd party kernel extensions.