If my current recommender recycles the letter from previous recommender after each other's consent, will this be classified as plagiarism?
This is for MS programs to US universities FYI.
Plagiarism pertains to academic output, not administrative documents, so formally this is not an issue.
That being said, admissions committees do receive all the documentation in a package for each applicant, and if I saw a package with two substantially identical letters, it would be a bit unusual.
In some cases, especially for admission at the Masters level in a not super competitive program and with an otherwise clearly strong application, reference letters are a formality. As long as they are moderately positive, all is fine, and therefore no one will really care if they are substantially identical. Frankly, having been on such committees, we may be happy enough if the required letters merely arrive on time and have sufficient content to reassure us that someone remembers the applicant at all!
However, if admission to the program is competitive, or if the application has some warning flags (grades, leaves, otherwise less strong than typical etc), it can be very much a wasted opportunity. In such cases, on committees we very much pay attention to letters to understand what makes the applicant special, and why the warning flags (if any) should not cause concern for the future. A letter indicating by its wording and enthusiasm genuine understanding of the student's situation carries a lot more weight. And we have all experienced that some recommenders seem to turn the dial to "gush" for everyone, without really meaning anything special (or perhaps truly in the heat of the moment believing every single one of the 30 students they've written for in the past 30 years are the best ever). Therefore 1+1>2 as far as two genuinely independent, complementary but different positive recommendations, and 1+1<2 for two that are bizarrely near-identical and indicate less than the usual amount of thought.
Final thought: on committees, we do realize that busy, jaded academics don't sit down and write every letter de novo. In particular if your recommender #2 is renowned, known to be busy, etc., it may be a feather in your cap that they were willing to "write" a letter for you at all, and similarities with #1 may well be overlooked.