It depends on, but is not limited to, the accent of the speaker. English dictionaries provide only the two standard pronunciations: RP and GenAm. In terms of pronunciation, don't take for granted everything you see in dictionaries, because they employ simplified transcription. Additionaly, words in dictionaries are pronounced in isolation.
To give weight to my arguments, the GenAm transcription of the word "man" doesn't take into account the /æ/ tensing process, and yet you can clearly hear the difference between the RP and GenAm pronunciations of the word man. Yet, both transcriptions have been transcriped the same: man Someone unaware of this process might incorrectly assume that in fact both pronunciations are the same.
Another example includes the flap T (the alveolar tap). Americans flap their Ts, and yet the flap T isn't transcribed, nor pronounced as /ɾ/. Why? Beats me.
Now, to answer your question, you would be better advised to check on the Internet the 3 varieties of unstressed vowels: schwa, schwi, and schwu. This article should shed some light on the issue and probably answer your question at least to some extent: https://en.wikipedia.org/wiki/Stress_and_vowel_reduction_in_English#Reduced_vowels_in_the_close_unrounded_area
I think the source of your confusion is that different people use different sets of symbols to represent the same pronunciations in English. Phonemic notation for English is fairly standardized, but it isn't absolutely uniform: for example, another area of variance is the notation of syllabic resonants (do we write the last syllables of button chasm bottle butter as /n̩ m̩ l̩ r̩/ or /ən əm əl ər/, or perhaps even /ᵊn ᵊm ᵊl ᵊr/?) and the notation of the "r" consonant sound (do we go with the simpler /r/ or the possibly more phonetically accurate /ɹ/?). In general, the difference between these is completely meaningless. Check the pronunciation guide of whatever resource you are using to learn what phonemic value some particular symbol represents.
When the schwa symbol <ə> is used in a stressed syllable, it almost certainly represents the STRUT vowel, even though this is standardly represented by /ʌ/. The "stressed schwa" notation for this vowel is probably most common in ad-hoc dictionary phonemic notation systems (I'd guess because it is more familiar to the general public than <ʌ>). Usually, notation systems that represent STRUT with <ə> will also represent NURSE with <ər>, <əɹ>, or <ɚ> (instead of <ɜr>, <ɜɹ>, or <ɝ>). It might not be entirely phonetically accurate, but neither is [ʌ] for many speakers (who may have a phonetic value more like [ɐ] or even [ə] instead).
This notation is possible without much, if any, ambiguity because schwa and STRUT are minimally contrastive at best, and actually in complementary distribution for many speakers. (See Accents of English by John C. Wells (who is also the author of the Longman Pronunciation Dictionary) for a description of this.)
The use of this notation in the Merriam-Webster dictionary was discussed at the following usingenglish.com forum thread: ə(unstressed) vs ʌ(stressed). The dictionaries you list evidently follow the same practice.
However, an earlier part of the Wikipedia article you referred to ("Vowels") defines the STRUT vowel as /ʌ/.
So the two sources simply use different definitions. The statement in the Wikipedia article is true, given the notation used there: it isn't true for all possible, or even for all existing phonetic notation systems used to transcribe English.
Note: I may be biased towards identifying /ə/ with /ʌ/ here because I do speak a dialect where "because" and "was" rhyme with "buzz," and "what" rhymes with "cut."
Peter Shor's explanation that it represents an unstressed weak form is also possible. It seems particularly likely for the Cambridge online dictionary; the evidence for it is that STRUT is usually represented by the symbol <ʌ> (I can't find any (other) word where /ə/ represents STRUT)
, and for "but," they distinguish "strong /bʌt/ weak /bət/." The transcription in general doesn't always seem to be consistent; in the UK dictionary, "muzzle" is transcribed as /ˈmʌz.l̩/ but "guzzle" is transcribed as /ˈɡʌz.əl/.
Best Answer
You need to keep a couple of things in mind:
The glyphs employed in the pronunciations you find in dictionaries are not "phonetic transcriptions" but phonemic representations (note that they are enclosed in //, not []). That is, they do not represent actual, infinitely variable acoustic phenomena but elements in the finite set of structurally categorized entities onto which hearers map what they hear. /z/ is the 'meaning' of the phone uttered, not its physical realization.
Pronunciation—physical realization—is environmentally conditioned: actual acoustic output of any phoneme is determined by the context in which it appears. With clothes, for instance, the voicing of the terminal /z/ will be sustained if the /z/ liaises with a following voiced phoneme but will slide off into /s/ if it liaises with a following unvoiced phoneme:
But what is heard in both cases, by a Real Hearer attending to the discursive meaning rather than the acoustic actuality, is the phoneme /z/.
The recorded pronunciations you find in dictionaries are artificially abstracted from context, like the wretched example sentences in grammarbooks and exams. But in practical terms there is no such thing as a 'null context' in Real Speech; the actual context of these pronunciations is a by-definition-voiceless silence following the phoneme /z/. So the Real Speaker slides off into the patent voicelessness which concludes these utterances.