敬語 consists of 尊敬語, 謙譲語 and 美化語.
お as a prefix can be either 尊敬語, 美化語 or neither.
The concepts of 尊敬語 and 美化語 are mutually exclusive, but お can be either 尊敬語 or 美化語. For example,
お/ご as a 尊敬語: お名前, お着物, お住まい, おビール, ご婦人, ご来店, ごゆっくり
(Can be only used to refer to something that belongs to your boss, etc)
お/ご as a 美化語: お箸, お菓子, お風呂, お片付け, ご禁制, ご大層
If these are really from two volumes of the same edition, I have to say this is indeed confusing and misleading. 食べた is perfectly valid in formal articles. As for the terminology, I see the following names most often:
だ: Plain form (can be formal or informal)
です: Polite form (usually formal, too)
(である: Literary/stiff form)
In Japanese, だ/である is called 常体 ...