Yes and no. Gifts can basically divided in three categories:
1) Special Gifts, which you can give only to certain character. So far I have noticed that all such gifts has special meaning to the character, usually linked to their past.
2) Gifts approved to that character. Each character has certain group of gift types they approve more, and thus giving such gift will result more approval points to you when given (around 5 points)
3) The rest. These gifts are just general gifts to that character, resulting only one or two points.
All gifts that doesn't belong to group number one can be given to any character, so that means they are "normal" gifts. Some characters like some gifts more than the others.
For example, the Tribal Necklace in the question belongs to both group number 2 and 3, as it depends on who you give it. As far as I remember Morrigan likes the necklace as much as Alistair, so both of them give you 5 points to approval rating. So it's not specifically to Alistair, and thus "normal" gift.
"As we all know, holy men were born during Christmas...
Like mr. Holopainen over there!" - Marco Hietala, the bass player of Nightwish
Special Gifts will ALWAYS result in dialogue (with a few exceptions, mainly dealing with gifts such as Andraste's Grace) with the character. For Alistair, two such are his Mother's Amulet, and Duncan's Shield. For Morrigan, it's a Gold Mirror and Flemeth's Grimoire are two such.
Approved Gifts will not result in dialogue, but will result in +10 to +6 Approval. two such are: The Bronze Statuette for Alistair, and a Gold Rope Necklace for Morrigan.
General Gifts would be like some rings, or the Steel Bracers. Generally a +5 to +1 for any.
Bones are for the Dog, and have no effect. I generally give the painted skyball to him as well.