[Galin]

In their Reader's Companion to The Lord of the Rings, Hammond and Scull noted:

"Elsewhere Tolkien equates Eldar with the High Elves ( . . . ) or defines the term more narrowly as "the West-elves" in contrast to the "East-elves", . . .).

There seems to be two definitions of High Elf: one (and the one seemingly more frequently employed by Tolkien) is equivalent to Tareldar -- and with respect to Middle-earth at least, the Tareldar are the returned Noldor.

Another use of the term "High Elves" seems to be basically equivalent to Eldar however, and thus includes the Sindar
-- at least arguably, given:

"In the beginning of this age many of the High Elves still remained. Most of these dwelt in Lindon west of the Ered Luin; but before the building of the Barad-dur many of the Sindar passed eastward, and some established
. . ."

Appendix B, Tale of Years

When Tolkien originally wrote the passage with Gildor, Frodo knew these were "High Elves" seemingly due to the name Elbereth. Yet the Sindar use this name, and the name is Sindarin. And if I read the signs rightly, when Tolkien wrote this passage the name Elbereth was "Noldorin" not Sindarin > in any case, after Tolkien changed the linguistic scenario we still have Frodo saying these are High Elves, as if Sindarin Elbereth is a sign of this. Some might say Tolkien forgot to revise Frodo's remark, but in my opinion it still works, given the suggestion from Appendix B.

Of course Gildor and Company turn out to be Exiles anyway, but Frodo's implication with respect to the name Elbereth need not be wrong.