My guess is that your book talks of "plain-form" when is referring to a style of speech. For example, in casual conversation you use the plain-form as opposed to the "polite-form" (普通形{ふつうけい} and 丁寧形{ていねいけい} respectively in Japanese).
In some cases this happens to be the same as the dictionary-form or 辞書形{じしょけい}. Specifically in the non-past and positive case:
For example:
Polite: 学校に行きます。
Casual: 学校行く。
In the second case you're using a plain-form that happens to be just the dictionary form. So there is no difference here.
However, in general the "plain-form" could be really anything. That is, whatever the conjugation of the verb you still call it "plain form". Using the same example as above:
Polite: 昨日、学校に行きませんでした。
Casual: 昨日、学校行かなかった。
So in this second example, the verb is in the the negative past plain form. So you notice that although this is still called "plain-form" it is not the same as the dictionary form in this case (the latter being 行く of course).
So, to resume:
Dictionary form: is the form of the verb as it is found in the dictionary (not surprisingly).
Plain form: it indicates a form of the verb that is generally used in casual/non-formal conversations and it includes present/past and affirmative/negative conjugations (in other words dictionary/root form, -nai, -ta, and -nakatta forms).
You can see more here.