Thanks. These are the actual canonical hours:
Vigils (nocturnal prayer)- only in religious communities, which if using the LOTH would use the Office of Readings. Some time during the night or anticipated the previous evening.
Lauds (Morning Prayer) (traditionally at sunrise, now usually around 6-8:30 am)
Terce (mid-morning prayer) (third hour of the day, usually around 8-10 am)
Sext (mid-day prayer) (6th hour of the day, usually around 11 am-1 pm)
None (mid-afternoon prayer) (ninth hour, usually around 2 to 4 pm)
Vespers (evening prayer) (traditionally at sunset, now usually between 4 and 7 pm)
Compline (night prayer) (prior to retiring; usually no later than 8 or 9 pm in monasteries, sometimes earlier).
These are approximate times, not written in stone.
Now with regards to which offices to say: for diocesan priests, they need only say
Office of Readings at a convenient time for them
Morning Prayer
Daytime Prayer
Evening Prayer
Night Prayer.
Daytime prayer has a quirk: it can be prayed at any one of the three daytime canonical hours, Terce, Sext or None. Only daytime prayer need be prayed by diocesan priests, at any one of the three daytime hours, selected at their convenience.
The Invitatory is an opening to the day’s prayer sequence. It consists of the invitatory verse (“Lord open my lips…”), followed by the Invitatory Psalm (traditionally, Ps. 94(95), but the LOTH also allows 3 other choices). The invitatory is prayed at the first office of the day, depending on whether it is the Office of Readings or Morning Prayer. If the former, the Invitatory is prayed with the verse and the psalm. If the latter, the verse is used but the psalm is optional. Contrary to popular misconception the Invitatory is not prayed before any other hour.
For religious communities that want to observe all three daytime hours, there is a complementary psalter in the LOTH consisting of the Gradual Psalms. Daytime prayer is prayed at one of the three hours, and the complementary psalms appropriate for the hour, at the other two.
For deacons, usually they are bound to a part of the LOTH, usually I think, in Canada and the US, Morning and Evening Prayer.
As laity, we’re not bound. We can do any part of it, or the whole lot if we feel up to it (I do the whole thing). But to be liturgical we must at least do our best to do it correctly and use the correct prayer for the time of day.
So both lists are correct, but the iBreviary omitted indicating the Invitatory (since it’s mobile), and omitted indicating the other daytime canonical hours, which are rarely prayed outside of choir.
Hope this helps. It looks complicated, but it really isn’t, once one gets into the right groove.