Which anthology's title means Collection of Ancient and Modern Japanese Poems?

The anthology whose title means “Collection of Ancient and Modern Japanese Poems” is the Kokin Wakashū.

Usually shortened to Kokinshū, it was Japan’s first imperial anthology of waka poetry. Emperor Daigo ordered its compilation, and it was presented around 905. The principal compilers were Ki no Tsurayuki, Ki no Tomonori, Ōshikōchi no Mitsune, and Mibu no Tadamine.

The collection contains about 1,100 poems arranged in 20 books, including sections on spring, summer, autumn, winter, love, travel, laments, and miscellaneous subjects. Its seasonal organization became enormously influential and helped shape later Japanese poetic traditions, including renga, haikai, and eventually haiku.

A common mix-up is Shin Kokinshū, whose title means “New Collection of Ancient and Modern Poems.” That later anthology was compiled in the Kamakura period, whereas Kokin Wakashū is the earlier, foundational imperial collection. Man'yōshū is older still, but its title has a different and debated meaning.