Are these forms different? If so, how do they differ? I would appreciate an example, thank you.
I am not 100% sure but I would guess that what you refer to as 普通形 is what in English is often translated as "casual" or "standard" conjugation as opposed to 丁寧形{ていねいけい} that is the "polite" form instead. This link seems to prove me right.
On the other hand, 辞書形｛じしょけい｝ is the so-called dictionary form and it's called this way because it is the form in which the verb is found in dictionaries.
To give a concrete example:
Verb: 買う｛かう｝- to buy
普通形: 買う (positive and non past. In this case this is the same as the dictionary form), 買わない (negative-non past), 買った (positive-past), 買わなかった (negative-past).
丁寧形: 買います (positive-non past), 買いません (negative-non past), 買いました (positive-past), 買いませんでした (negative-past).
辞書形: It's just 買う. This is how you find the verb "to buy" in any dictionary. You can see it as a non-conjugated basic form as it could be the infinitive in English (in dictionaries you find "buy", not "bought" for example).
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@MXMLLN well I suppose you can call it that way as well. Not sure what’s the best translation in English but I guess it’s clear what we are talking about here. – Tommy Jan 17 '18 at 3:50
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辞書形, in fact, is part of 普通形, which consists of four different forms, including the 〜た form (past affirmative), the 〜なかった form (past negative), the ~ない form (nonpast negative) and finally the root form, a.k.a. 辞書形 (nonpast affirmative). For example, what the root form, 辞書形, is for a verb is much like what "be" is for "is", "are", "was", etc. You can find more detailed explanation here and here.
