Yes the difference is remarkable. Census is complete enumeration. All elementary units in the population are studied.
On the other hand, consecutive sampling involves including into the sample all available units satisfying the inclusion criterion until the desired sample size is obtained. This is a non-probability sampling method.
These are 2 completely different samling methods. Census requires collection of data for the total population and is practically difficult to apply unless you have a very specific case study where population is manageable. On the other hand consecutive sampling requires that you have firstly calculated the required sample size by a known formula based on propotion or st. dev. of continous variables in a pre-sampling process.
In addition what is said by scientists above, consecutive ssmpling is selection of portion of population based on availability in a given time bound from a continously available population, Census is capturing the entire source population.