A schwa is an unstressed vowel sound. It is represented by the symbol ə.
Most often, people only talk about the sound /ŭ/ when they are talking about schwa, and that makes sense because this is a very common sound. However, in reality English has more than one schwa sound; or perhaps it would be more accurate to say that the schwa sound can take a variety of shapes.
At LOE, we teach schwa to students as a "lazy" sound, because you barely have to move your mouth to say it. That is why it happens in unstressed syllables and words.
Often the schwa sound is closest to /ŭ/, but in some words the unstressed vowel is pronounced with a sound closer to /ĭ/. This makes sense, because that sound is also "lazy" - the mouth moves only a little to pronounce it, especially if you are already forming a sound that is high and forward in the mouth, like /t/ or /s/, before the sound or after it in a word. That's because next to those sounds, it's easier to say /ĭ/, which is formed in a similar part of the mouth, than to say /ŭ/.
Trumpet, roses, precise, minute...