A participial phrase starts with a participle.
A prepositional phrase starts with a preposition.
A participial phrasei starts with either a participle or a particple. It acts as an adjective .
ex: The boy frightened by the thunder ran to his mother.
ex: Shivering with cold the man wandered through the forest.
A prepositional phrase starts with a preposition and is followed by an object. A prepositional phrase acts either as adjective or adverb .
ex: The lady between the two men is my aunt.
ex: The bird perched on the branch .
Note: Notice that a participle followed by a prepositional phrase becomes a participial phrase.
ex: 1. frightened by the thunder
frightened — past participle
by the thunder — prepositional phrase
ex 2. shivering with cold
shivering — present participle
with cold —prepositional phrase