What do these two terms mean on the data entry grid?
Check out this Glossary on Indexing terms:
Bottom line - the image is a picture of a document that Indexers examine to extract info (into fields - e.g. name, birthdate, etc) from records about individuals and type that info into fields in an entry. So an entry is a digitized version of a record, extracted from an image.
The term “field” is used to describe the components of a “record” (on the image) and of an entry. On an “entry” a field is a named box on a form into which you type info extracted from the image (e.g. age). On a “record” it is the written version of that information (e.g. age) found on the image.