การใช้ภาษาอังกฤษ ที่ถือว่าถูกต้องในที่นี้ อ้างอิงตามมาตรฐานของภาษา
These 2 words are nearly the same in meaning.
I think 'consecutive' is used to say 'in series' of a "known" order. For examples:' days of week' is a known order. Months of year, 1 2 3 ..., 2015 2016 2017...,... are known order.
This is derived from 'sequence': sequential -- one after/following another in a sequence.
'successive' is used to say a 'continuation of many' events/things -- without a gap/break.
But it is quite difficult to make a 'rule'. We may have to learn by observing/copying their use.