Does Strahd's unarmed strike deal full damage if used to grapple?

In the Roll20 electronic version of Curse of Strahd, Strahd's stat block has been updated at least twice, in patches 1.9 (June 2020) and 1.3.

The current version (June 2020) reads:

Unarmed Strike (Vampire or Wolf Form Only)
Melee Weapon Attack: +9, Reach 5 ft, one target
Hit: (1d8+4) slashing damage plus 14 (4d6) necrotic damage
If the target is a creature, Strahd can grapple it (escape DC18) instead of dealing the bludgeoning damage.

This appears to me to follow the most recent revision of CoS, 6th Printing, published 06/17/2020, available at https://www.dndbeyond.com/forums/dungeons-dragons-discussion/rules-game-mechanics/8760-official-wizards-of-the-coast-errata#c16.

That this version matches yours, and is different from the earlier print version of CoS shown in Thomas Markov's answer, may mean that yours is actually the currently most correct version, but does little to clarify whether Strahd should be doing slashing or bludgeoning damage. However, I think it is safe to say that the "instead of" indicates that Strahd's grapple should do necrotic damage, only, regardless of what his unarmed strike does.

For reference, the current version of the Vampire statblock reads:

Unarmed Strike (Vampire Form Only): Melee Weapon Attack: +9 to hit, reach 5 ft., one creature.
Hit: 8 (1d8 + 4) bludgeoning damage. Instead of dealing damage, the vampire can grapple the target (escape DC 18).

(The 5th Edition SRD and the Vampire stat block within CoS differ only in some punctuation.)

The current version of Vampire Spawn reads:

Claws: Melee Weapon Attack: +6 to hit, reach 5 ft., one creature.
Hit: 8 (2d4 + 3) slashing damage. Instead of dealing damage, the Vampire can grapple the target (escape DC 13).

(The 5th Edition SRD and the Vampire Spawn stat block within CoS differ only in some punctuation)

My printing of Curse of Strahd (purchased new this year) states that unarmed strike deals bludgeoning damage:

Therefore, Strahd’s grapple would still deal the 4d6 necrotic and not the bludgeoning.

This is notably inconsistent with DnDBeyond which says that Strahd’s unarmed strike deals slashing.

Melee Weapon Attack: +9 to hit, reach 5 ft., one target. Hit: 8 (1d8 + 4) slashing damage plus 14 (4d6) necrotic damage. If the target is a creature, Strahd can grapple it (escape DC 18) instead of dealing the slashing damage.

But, DnDBeyond also says “instead of dealing slashing damage”, so according to these two sources, Strahd’s grapple only deals necrotic damage.

User David Coffron has reported that the first printing of Curse of Strahd is also consistent with the image of my recent printing shown above.

The discrepancy between DnDBeyond and the printed sourcebook can be attributed to this errata posted by DnDBeyond on June 19, 2020:

Strahd von Zarovich (p. 240). In the stat block, change "Unarmed Strike (Vampire Form Only)" to "Unarmed Strike (Vampire or Wolf Form Only)," and in the unarmed strike, change "bludgeoning" to "slashing." Also change "Bite (Bat or Vampire Form Only)" to "Bite."

This errata from DnDBeyond coincides with this statement from WoTC that they intend to make some changes to Curse of Strahd. It seems likely that DndBeyond’s errata is a preview of what will eventually appear in the printed sourcebook.