The difference between Continuous and Stepwise

When used as adjectives, continuous means without stopping, whereas stepwise means one (small) step or stage at a time.

Stepwise is also adverb with the meaning: one step or stage at a time.

check bellow for the other definitions of Continuous and Stepwise

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.

Stepwise as an adjective:

One (small) step or stage at a time; gradual; piecemeal