The difference between an adverbial phrase and a prepositional phrase lies in their roles and structures in a sentence, though they can sometimes overlap. 

1. Adverbial Phrase

• Definition: A group of words that functions as an adverb to modify a verb, adjective, or another adverb.

• Purpose: Adverbial phrases provide more detail about how, when, where, why, or to what extent something happens.

• Structure: Adverbial phrases can be made up of various components, including prepositional phrases, adverbs, or other descriptive words. They aren't limited to a single structure.

Examples of Adverbial Phrases:

• With a smile – She sang with a smile. (modifies the verb sang by describing how she sang)

• At the end of the day – He decided, at the end of the day, it was time to rest. (modifies the verb decided by specifying when)

• In a hurry – She left in a hurry. (modifies the verb left by describing how she left)

2. Prepositional Phrase

• Definition: A group of words that begins with a preposition and ends with a noun or pronoun (the object of the preposition), along with any modifiers of that noun or pronoun.

• Purpose: Prepositional phrases provide more information about the relationship between objects or actions in the sentence, often modifying nouns or verbs. They can describe place, time, direction, or other relationships.

• Structure: A prepositional phrase always starts with a preposition and ends with an object, and may include modifiers.

Examples of Prepositional Phrases:

• On the table – The book is on the table. (modifies book by telling where it is)

• By the window – She sat by the window. (modifies sat by telling where she sat)

• Under the bed – The shoes are under the bed. (modifies shoes by telling where they are)

Key Differences:

1. Role in the Sentence:

   • An adverbial phrase modifies verbs, adjectives, or other adverbs, answering questions like how, when, where, why, or to what extent.

   • A prepositional phrase typically modifies nouns or verbs, providing information about the relationship between those words, such as place, time, or direction.

2. Structure:

   • An adverbial phrase may or may not contain a preposition. It can be more flexible, involving adjectives, adverbs, or other words.

   • A prepositional phrase always contains a preposition and its object (noun or pronoun), with potential modifiers.

Overlap:

• A prepositional phrase can function as an adverbial phrase when it modifies a verb (telling where, when, how, or why).
  Example:

  • She jumped over the fence. (Prepositional phrase modifying jumped by telling how or where she jumped)

  • They met at noon. (Prepositional phrase modifying met by telling when they met)

But not all adverbial phrases are prepositional phrases, as some adverbial phrases don’t require prepositions to function.