"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.