/ʌ/ up, mother, mud
/ə/ about, animal, problem, circus
Are these two sounds same? If different, tell me please what's the difference, please
Dictionaries consider all those as schwas. In reality, they are reduced vowels, which can be more or less "central", depending on the stress, the speed, the accent.
So dictionaries usually indicate the "e" and the final "a" in NEVADA with the same symbol, the schwa, but in reality those two sounds are different (or at least they are so to me). I think the latter is a lower vowel.
I'm afraid there's no rule of thumb for you though. I can only suggest you treat them as reduced "kind-of-central" sounds, and then adjust them depending on the speed of your speech, the consonant that follow, the accent you want to pick up, etc. The only way to do this is by listening a lot, and picking up "the sound" of English. And since it depends on the dialect, there are lots of differences, so it depends what variety you are trying to learn.
For example, the capitalized letters in About, animAl, and problEm, they are all slightly different from each other to me, despite being called schwas.
That said, I am a non-native speaker, LOL. :-)
I wouldn't consider the vowel in "up" to be a schwa or a reduced vowel: in most dialects it's realized as something between [ʌ] and [ɐ], a bit opener and sometimes a bit backer than a schwa. Of course, the schwa itself can be variable, and in some dialects I think the final schwa especially can be rather open. As for the first syllable of Nevada, that may be pronounced as [ɪ] or [ə].
only in 'about' do I pronounce the 'a' somewhat like a short 'u' ("cup" Amer.), but less distinctively. More like a true schwa.
The 'u' in 'cirus' I pronounce like a short 'i' /s3:kis/