There is a whole spectrum of reasons for differences in signing "styles" ranging from levels of fluency, emotiveness, and differences in background. The least "animated" in your description may have learned to sign SEE, which is actually signed English, not ASL, while native signers or Deaf-of-Deaf signers may tend to be more skilled in communicating with facial expressions and movement indicating intonation, duration, temporality/grammatical functions, and emphasis.
You're correct that body orientation and movement have meaning, as do "choppiness" and repetition. English does similar things with sound-- think about how, when you speak, these have different meanings:
She said that.
SHE said that.
She SAID that.
She said THAT.
She said that?
SHE said that?
She SAID that?
She said THAT?
Or signs carry meaning in this kind of way:
SHE READ signed slowly, head tilted forward, brow furrowed, mouth pursed, might translate as "She read, slowly and laboriously."
SHE READ signed elliptically and repeatedly without stopping, head tilted back slightly, confident facial expression, might translate as "She read skillfully and continuously for a long time."
SHE READ signed repeatedly with a slight pause at the conclusion of READ, head tilted, mouth puffing out or exposing the tongue might translate as "She read many, many times, exhaustedly."
So yes, you're right that urgency and scope of a situation are certainly communicated with the same kind of movements and expressions.