The difference between Constant and Continuous

When used as adjectives, constant means unchanged through time or space, whereas continuous means without stopping.

Constant is also noun with the meaning: that which is permanent or invariable.

check bellow for the other definitions of Constant and Continuous

Constant as an adjective:

Unchanged through time or space; permanent.
Constant as an adjective:

Consistently recurring over time; persistent.
Constant as an adjective:

Steady in purpose, action, feeling, etc.
Constant as an adjective:

Firm; solid; not fluid.
Constant as an adjective (obsolete):

Consistent; logical.

Constant as a noun:

That which is permanent or invariable.
Constant as a noun (algebra):

A quantity that remains at a fixed value throughout a given discussion.
Constant as a noun (science):

Any property of an experiment, determined numerically, that does not change under given circumstances.
Constant as a noun (computing):

An identifier that is bound to an invariant value; a fixed value given a name to aid in readability of source code.

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.