As I have told you, I have little formal education in music. It seems to me, however, that a number of "modern" conductors change the timing of music to enhance its lyricism and power. By lengthening some notes and shortening others, as well as silences between notes, they find interpretations that are often more "romantic."
Although there are composers like Carlos Klieber (recognized by other conductors as perhaps the best conductor of the 20th century) who stick to the score with rigorous timing, but somehow enhance a piece of music to its utmost. Kleiber's recording of Beethoven's Fifth is a good example. His timing seems to my ear to be exacting, yet you cannot find a classical forum that does not list him as one of the best, if not the best, conductor of Beethoven's Fifth. I have also found this to be true of Karl Bohm. I have a record set of him conducting Mozart's later symphonies and also Beethoven's 6th. He is the only conductor whose 6th I enjoy as much as Bruno Walter's.
I have read that different historical periods produce different types of musical interpretations. I have seen a number of performances, as well as owning a number of recordings, by musicians who "deconstruct" a musical score and reconstruct it with very "modern" interpretations. I have heard Mirga Grazinyte-Tyla, (whom I believe will be one of the 21st centuries great conductors) tear apart Tchaikovsky's Violin Concerto and produce something which I wouldn't have recognized, at least in some passages.
I have a boxed set of Fazil Say playing Mozart's piano concertos and he changes timing and dynamics in drastic ways which to my ear convey the "story" that I think @mahgister was talking about.
Hopefully @frogman will weigh in.