The difference between Continuous and Discrete

When used as adjectives, continuous means without stopping, whereas discrete means separate.

check bellow for the other definitions of Continuous and Discrete

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.

Discrete as an adjective:

Separate; distinct; individual; non-continuous.

Examples:

"a government with three discrete divisions"
Discrete as an adjective:

That can be perceived individually and not as connected to, or part of something else.
Discrete as an adjective (electrical engineering):

Having separate electronic components, such as individual diodes, transistors and resisters, as opposed to integrated circuitry.
Discrete as an adjective (audio engineering):

Having separate and independent channels of audio, as opposed to multiplexed stereo or quadraphonic, or other multi-channel sound.
Discrete as an adjective (topology):

Having each singleton subset open: said of a topological space or a topology.
Discrete as an adjective:

Disjunctive; containing a disjunctive or discretive clause.

Examples:

"I resign my life, but not my honour" is a discrete proposition."