As adjectives the difference between consecutive and continuous is that consecutive is following, in succession, without interruption while continuous is...
Continuousas anadjective(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: ...
As adjectives the difference between continuous and consistent is that continuous is without break, cessation, or interruption; without intervening time while consistent is...