The difference between Singular and Unique

When used as nouns, singular means a form of a word that refers to only one person or thing, whereas unique means a thing without a like.

When used as adjectives, singular means being only one of a larger population, whereas unique means being the only one of its kind.

check bellow for the other definitions of Singular and Unique

Singular as an adjective:

Being only one of a larger population.

Examples:

"A singular experiment cannot be regarded as scientific proof of the existence of a phenomenon."
Singular as an adjective:

Being the only one of the kind; unique.

Examples:

"She has a singular personality."

"rfquotek Francis Bacon"
Singular as an adjective:

Distinguished by superiority; eminent; extraordinary; exceptional.

Examples:

"a man of singular gravity or attainments"
Singular as an adjective:

Out of the ordinary; curious.

Examples:

"It was very singular; I don't know why he did it."
Singular as an adjective (grammar):

Referring to only one thing or person.
Singular as an adjective (linear algebra, of matrix):

Having no inverse.
Singular as an adjective (linear algebra, of transformation):

Having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
Singular as an adjective (set theory, of a cardinal number):

Not equal to its own .
Singular as an adjective (legal):

Each; individual.

Examples:

"to convey several parcels of land, all and singular"
Singular as an adjective (obsolete):

Engaged in by only one on a side; single.

Singular as a noun (grammar):

A form of a word that refers to only one person or thing.
Singular as a noun (logic):

That which is not general; a specific determinate instance.

Unique as an adjective (uncomparable):

Being the only one of its kind; unequaled, unparalleled or unmatched.

Examples:

"Every person has a unique life, therefore every person has a unique journey. ― Gary Cook"

"synonyms: one of a kind sui generis singular"
Unique as an adjective:

Of a feature, such that only one holder has it.
Unique as an adjective:

Particular, characteristic.
Unique as an adjective (proscribed):

Of a rare quality, unusual.

Unique as a noun:

A thing without a like; something unequalled or unparallelled.