I noticed that if I use the regular search to look for a portion of a word or numbers that I do not get any results back.
For example, if I have a Task that contains a number "00123456" in the Task Name, but I use "123456" in the regular search, it doesn't find my Task.
Second example, If I have a Project that contains "Waterfall" in the name, but I use "fall" in the regular search, it doesn't find my Project.
This applies to regular search in both Classic and New Experience. Advanced Search seems to handle portions of names, regular search should work the same as advanced search as most of our users will rely on regular search....they won't necessarily use the Advanced Search.