I think it would be best to avoid trying to talk about meaning in terms of voice at all. It's confusing, like talking about time reference in terms of "tense", because people often use terms like "voice" and "tense" to refer to purely morphological categories. I would advise only using the term "voice" to talk about the morphological form of verbs, since that seems easier to determine. There are so many different types of thematic relations that a complete classification of verbs according to their meanings would need much more than two or three categories.
English only distinguishes two forms that I am aware of for voice: active and passive. Some verbs have an intransitive construction that is sometimes called "middle voice" or "mediopassive" due to its meaning, although it takes the form of the active voice: things like "the water froze" (vs "the cold of the night froze the water") and "the water boiled". While these words are maybe valid as technical terminology with defined meanings as applied to English, I don't think it is particularly wise to use this terminology to associate the English expressions with Greek expressions, or with other English verbs with somewhat similar meanings like "catch". My impression is that the thing called "middle voice" in Greek is not really the same as the thing that some people call "middle voice" in English.
When people say that Greek deponent verbs are "active in meaning", I hope the main point they're trying to make is that they cannot be converted into an active-voice equivalent. I don't speak Greek of any kind, but that is what I gather from the Wikipedia article Ancient Greek verbs. The sources I have looked at also indicate that Greek distinguishes between a passive and middle voice in the inflection of the aorist (although not in the present, imperfect, or perfect), and some deponent verbs have passive-voice aorist forms while others have middle-voice aorist forms; so it seems like the description of deponent verbs as "passive in form" is a bit of a simplification (although passive-form deponents are apparently more common than middle-voice deponents).
A less charitable interpretation that I've seen in some of the sources referenced below is that "active in meaning" is simply based on the fact that Greek deponent verbs are often translated into English using English active-voice verbs—this would be an erroneous basis for a description of Greek grammar, since a description of a term used in Greek grammar should not be defined based on English categories of voice.
Anyway, I agree with you that this common definition of "deponent" seems like sloppy, unnecessary wording.
So, I would recommend saying something like
Although some describe Greek deponent verbs as 'active in meaning', I do not agree with this description. The distinction between deponent verbs and non-deponent verbs is simply that
deponent verbs have no active-voice forms. [optionally specify what time period or corpus you are talking about here e.g. a number of sources I found talking about Biblical Greek specify "no active-voice form found in the Greek New Testament"]
non-deponent verbs have active-voice forms.
The meaning of a deponent verb, like the meaning of any verb, depends on the specific word.
This description also seems in line with some resources I found online talking about Greek deponent verbs: