In SharePoint fields have display names and internal names. Created By or Modified By are display names of fields. Internal names are used when creating queries. Author is the internal name of Created By field and Editor is the internal name of Modified By field.
UPDATE
One way to check the internal name of a field from SharePoint UI is to go into List Settings and Click on the Column Name e.g. Modified By in Columns section. Observe the Url in the browser. It will be something like this:
http://aissp2013:111/_layouts/15/FldEditEx.aspx?List=%7B98089921%2D96C3%2D4B8C%2DB5D0%2D593360EFD1DA%7D&Field=Editor
At the end of the url is &Field=Editor which gives the internal name of the column.
However, as your question is regarding Search Service, this is how you should try to set up your CreatedBy and ModifiedBy managed properties in Search:
Go to Search service application in SharePoint Central administration site and click on Search Schema. Check the crawled properties of Author and Created By managed properties. You may need to add Office:4(Text) crawled property to Created By managed property. This is what I had to do long time before in SharePoint 2010. Similarly search the managed property EditorOWSUSER and notice the crawled property it is mapped to and then add that crawled property to ModifiedBy managed property.