Christina's last known location of Burghead I believe to be in the area of Moray, Elgin or Banffshire. Have never researched the location in my own tree so a little unfamiliar with that area as of now. I think "Grantown" is actually "Grantown on Spey". There does appear some overlap with Duthil, Elgin and Moray. Which can be confusing.
Indeed.
Burghead is in the parish of Duffus in the county of Moray aka Morayshire. In the 19th century Moray was officially known as the county of Elgin, or Elginshire, after its county town, Elgin, which is in the parish of Elgin. Fortunately the old name was restored by Act of Parliament in 1928, but when you come across a reference to 'Elgin' you have to look closer to see whether the reference is to the town, the parish or the county.
Grantown is indeed Grantown-on-Spey. It is in the parish of Cromdale Inverallan and Advie, most of which is in Moray but there is part of it in Inverness-shire. This parish was formed by the union of the three older parishes, hence the unwieldy name. It is often referred to as simply Cromdale for short. Grantown is in the part that was formerly the parish of Inverallan.
The parish of Duthil is in Inverness-shire, but it is next door, on the south-west, to Cromdale Inverallan and Advie.
The parish of Inveravon in the county of Banff aka Banffshire is next door to Cromdale Inverallan and Advie on the north.
You might find
http://www.genuki.org.uk/big/sct useful for sorting out these and similar geographical conundrums.