I think SeaBees was a term used by upper classmen for entry level (E-1)
Seaman Recruits, although it well may have been the E-2 Seamen Apprentices. It's not clear to me if Recruits are in the general training course (which was about 6 weeks to 2 months when my brother went in in 1965) or if it referred to actual first-timers on a Naval vessel, Seamen Apprentices.
Seabee is a term used to refer to those in the Construction Battilion, which is one of the 4 different apprenticeship classifications. They are Seaman (working on surface ships), Airman (working with aircraft and maintenance on them), Fireman (working mainly in engineering rates), and Constructionman (working with the SeaBees).
Airman have blue stripes, Firemen have red stripes, Seaman have white stripes, and Constructionmen have green. That is how you tell what apprenticeship they have entered into, by the color of their stripes.
As far as E-1 through E-3? One stripe denotes an Seaman Recruit, two stripes denote a Seaman Apprentice, and 3 stripes mean they are a full fledged Seaman. In the other apprenticeships you would use Fireman, Airman and Constructionman instead of Seaman. Generally when referring to a person who is E-3 and below, you would use the terms "recruit", "apprentice" and "Seaman" or whatever apprenticeship their stripes say they are.
As far as referring to someone who is a newbie? If you are in the surface Navy, you generally refer to them as "boot". If you are in the aviation Navy, newbies can also be called "FNG's", which stands for ******* New Guy.
Spent 20 years in the Navy as a Personnelman, and also worked at a MEPS (Military Entrance Processing Station) as Head Classifier for the last 2 years of my career, which means that I assigned people jobs based on availability and their qualifications.