From Google dictionary:
Interestingly, when you look up "shiver," "tremble" is given as a synonym, but not vice versa.
shiv·er
verb
1. (of a person or animal) shake slightly and uncontrollably as a result of being cold, frightened, or excited.
"they shivered in the damp foggy cold"
synonyms: tremble, quiver, shake, shudder, quaver, quake
noun: shiver; plural noun: shivers
1. a momentary trembling movement.
"she gave a little shiver as the wind flicked at her bare arms"
trem·ble
ˈ
verb
1. shake involuntarily, typically as a result of anxiety, excitement, or frailty.
"Isobel was trembling with excitement"
synonyms: shake, shake like a leaf, quiver, twitch, jerk;
2. be in a state of extreme apprehension.
"I tremble to think that we could ever return to conditions like these"
synonyms: be afraid, be frightened, be apprehensive, worry, shake in one's boots; More
(of a person's voice) sound unsteady or hesitant.
3. shake or quiver slightly.
"the earth trembled beneath their feet"
synonyms: shake, shudder, quake, wobble, rock, vibrate, move, sway, totter, teeter;
noun
noun: tremble; plural noun: trembles; plural noun: the trembles
1. a trembling feeling, movement, or sound.
"there was a slight tremble in his voice"
synonyms: tremor, shake, shakiness, trembling, quiver, quaking, twitch, vibration, unsteadiness More
antonyms: steadiness
2. informal
a physical or emotional condition marked by trembling.