The difference between Continuous and Unceasing

When used as adjectives, continuous means without stopping, whereas unceasing means continuous.

check bellow for the other definitions of Continuous and Unceasing

Continuous as an adjective:

Without stopping; without a break, cessation, or interruption

Examples:

"synonyms: nonstop"

"a continuous current of electricity"
Continuous as an adjective:

Without intervening space; continued

Examples:

"synonyms: protracted extended"

"a continuous line of railroad"
Continuous as an adjective (botany):

Not deviating or varying from uniformity; not interrupted; not joined or articulated.
Continuous as an adjective (analysis, of a [[function]]):

Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D.
Continuous as an adjective (mathematics, more generally, of a function between two [[topological space]]s):

Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).

Examples:

"Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected."
Continuous as an adjective (grammar):

Expressing an ongoing action or state.

Unceasing as an adjective:

continuous; continuing indefinitely without stopping