The day meal of Shabbat has a different texture than the evening meal. Friday night is the dramatic entrance, candles, Kiddush, the descent of the Shechinah, the family gathered around the table after synagogue. Saturday day is the abiding mood, Shabbat already underway, the morning service over, the sun high. The lunch is unhurried; the singing reflects that.
Friday-night zemirot frequently use language of mystical union (bride/groom). Saturday-day zemirot focus more on the practice of Shabbat, what observing Shabbat means, what the rest accomplishes, how the soul is restored. Less ecstatic, more meditative.
Medieval Hebrew poets routinely hid their names in the first letters of stanzas, a tradition that allowed authorship to be preserved even when names were dropped from titles or worn off old manuscripts. Baruch El Elyon, Ki Eshmera Shabbat, and several others have such acrostics. Yedid Nefesh hides the divine name (yud-heh-vav-heh) in the same way; Lecha Dodi hides the name of the author Shlomo HaLevi.
If you read a zemer slowly and check the first letter of each stanza, you'll often find the author's signature hidden in the page. It's like a secret thumbprint, ~800-1000 years old.
Most modern benchers (the booklets used at Jewish tables) print 4-6 Saturday-day zemirot, often the same ones across communities. Baruch El Elyon is universal. The order and selection vary slightly by rite: Ashkenazi siddurim emphasize Baruch El Elyon and Yom Zeh Mechubad; Sephardi siddurim often start with Yom Zeh L'Yisrael; Yemenite communities preserve some unique Saturday-day songs not found in other rites.
The melodies are folk-traditional; many have Hasidic or Mizrahi modern reinterpretations. Spend a few Shabbat lunches with a family that sings, and you'll absorb the corpus within a month.