I'm not sure that these terms are standard. Generally consecutive numbers means number sthat are next to each other in the whole numbers, or integers, 1, 2, 3, 4, ... none missing in the middle. A sequence is just a set of numbers. Any set of numbers. So technically seqquential numbers would mean the next number in the sequence. The most common sequence people think of would be the integers, whole numbers, so often it probably means the same thing. Technically could be anything, the serial number on a banknote for example. . Sequential numbering of something means putting the number on something using consecutive numbers, such as numbering tickets form 1000 to 2000, not missing any out.

John, thank you a lot! It seems clearer for me!

Consecutive means anything that follows one after the other with no gap, it is not restricted only to numbers. The alphabet A, B,C-->to Z is consecutive. there is no gap in the sequence. The days of the week Monday, Tuesday -->to Sunday are consecutive. 1,2,3,4,5,6,7,8,9,10,11,12 --> is consecutive. "it rained continuously for six consecutive days" = it rained with no gaps in the days for six days continuously. Money ,Tuesday , Wednesday, Thursday, Friday and Saturday and stopped on Sunday. Sequential meanings anything that follows a Sequence for numbering of things like invoices, banknotes there is overlap. Because anything that continues in the correct or expected order is grammatically both consecutive and sequential. The odd numbers 1,3,5,7,9,11,13 are sequential. So too are the even Numbers 2,4,6,8,10,12 Bank notes leave the mint in sequential order because they have numbers and letters that make up the identifying sequence when leaving the print machines, but they are sold and collected as being in consecutive order where a collector has two in the correct order one after the other with no gap.