The R package is 'secr' not SECR. I assume you refer to the function 'closure.test'. As you would discover from reading the help page, closure.test defaults to exactly the same test as CAPTURE (i.e. the Otis et al 1978 test). You do not give an example.
For the default dataset in DENSITY, CAPTURE gives
Overall test results --
z-value -1.408
Probability of a smaller value 0.07949For the same dataset in 'secr'
closure.test(captdata)
statistic p
-1.40849 0.07949
I don't know what you are talking about. The Stanley & Burnham test may be selected as an option in closure.test. None of the above should be taken to indicate I think closure tests are necessary or informative.
Murray