"morgens" is round about the time you get up (assuming you get up at some point between, say, 5 and 8 or 9 at the latest). "vormittags" is more or less the time between getting up and 12 o'clock noon (mittags).

"Morgen" lasts until about 10 o'clock and then "Vormitag" lasts until about 12 o'clock. However, you say "Guten Morgen!" - from midnight until 12 o'clock, because there's no "Guten Vormittag!".