\"In the very same vein as\" is the most common idiom through a long shot.
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The other alternatives \"in a comparable vein to\" and also \"along the very same vein\" sound a little odd to mine ear.
I guess: v you\"d be better off using \"in a similar method to\" and also \"along the very same lines\" instead.
Following from Elian\"s answer, the usage of Google books trend viewer to be excellent, however left me perplexed - \"in similar vein\" sounded like the more common alternative to me.
It turns out, the preposition in ~ the end of the expression is important. If you perform the same search without \"to\" or \"as\", then you get, indigenous most typical to the very least common:\"In a similar vein\"\"In the same vein\"(almost no one in comparison to the others) \"Along a comparable vein\"
This to adjust closer to my gut feelings. The difficulty is that as soon as used, this idioms are usually offered as a comparison. So for example: \"The cat satellite on the mat; in a comparable vein, the frog satellite on the log\", or, \"His grandma took trip to Africa and truly uncovered herself - and in the very same vein, the journeyed to Australia in the hope that he can truly come to be himself.\".
In answer to the question about difference in meaning, I would argue it is negligible. Same is stronger than similar, but the idiom is about finding a commonality between two different scenarios, and also I don\"t think there is any type of objective test the you can do to recognize whether very same or similar is ideal to her situation, and also I can not think of a circumstance where one would certainly be wrong and the various other right.
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I\"ve ignored the 3rd one due to the fact that I think, in this case, you can make a instance for saying that where there is an ongoing transition, \"along a similar vein\" would be an ext appropriate. For example. \"Jon focussed his investigation on hookers and also drug dealers; Betty ongoing her examination along a comparable vein\". In this usage, i imagine you can find the idiom an ext often close come the finish of the sentence.