Yes, both in characteristics and history.
Starting from here,
Another writer, Wirt Sikes wrote in the British Goblins (1880), comparing the Welsh fairies with that of Norse/Teutonic fairies.
Sikes says that there are four types in the Norse tradition:
- dwarves and troll,
- nisses and
- necks, mermen, and mermaids.
While in the Welsh traditions there are:
- The ellyllon, or the elves;
- The coblynau, or the mine fairies;
- The bwbachod, or the household fairies;
- The gwragedd annwn, or the fairies of the lakes and streams;
- The gwyllion, or the mountain fairies.
Here, the classification of Welsh fairies distinguished household fairies from that of the mines, lakes and mountains. Like the Irish tradition, the Welsh can be further divided into solitary and social fairies.
I found the text of British Goblins, where Sikes states (at the start of Chapter II)
Fairies being creatures of the imagination, it is not possible to classify them by fixed and immutable rules. In the exact sciences, there are laws which never vary, or if they vary, their very eccentricity is governed by precise rules. Even in the largest sense, comparative mythology must demean itself modestly in order to be tolerated in the severe company of the sciences. In presenting his subjects, therefore, the writer in this field can only govern himself by the purpose of orderly arrangement. To secure the maximum of system, for the sake of the student who employs the work for reference and comparison, with the minimum of dullness, for the sake of the general reader, is perhaps the limit of a reasonable ambition. Keightley divides into four classes the Scandinavian elements of popular belief as to fairies, viz.:
- The Elves;
- The Dwarfs, or Trolls;
- The Nisses; and
- The Necks,  Mermen, and Mermaids.
How entirely arbitrary this division is, the student of Scandinavian folk-lore at once perceives. Yet it is perhaps as satisfactory as another. The fairies of Wales may be divided into five classes, if analogy be not too sharply insisted on. Thus we have
- The Ellyllon, or elves;
- The Coblynau, or mine fairies;
- The Bwbachod, or household fairies;
- The Gwragedd Annwn, or fairies of the lakes and streams; and
- The Gwyllion, or mountain fairies.
"Keightley" refers to Thomas Keightley, the author of Fairy Mythology, from 1870. I found an index of all its parts. This is certainly harder to search through, but in his analysis on Ireland, Keightley writes
The fairies of Ireland can hardly be said to differ in any respect from those of England and Scotland. Like them they are of diminutive size, rarely exceeding two feet in height; they live also in society, their ordinary abode being the interior of the mounds, called in Irish, Raths (Rahs), in English, Moats, the construction of which is, by the peasantry, ascribed to the Danes from whom, it might thence perhaps be inferred, the Irish got their fairies direct and not vid England.
In the more general summary of Celtic fairies, he writes
Yet in the popular creed of all these tribes, we meet at the present day beings exactly corresponding to the Dwarfs and Fairies of the Gotho-German nations. Of these beings there is no mention in any works--such as the Welsh Poems, and Mabinogion, the Poems of Ossian, or the different irish poems and romances--which can by any possibility lay claim to an antiquity anterior to the conquests of the Northmen. Is it not then a reasonable supposition that the Picts, Saxons, and other sons of the North, brought with them their Dwarfs and Kobolds, and communicated the knowledge of, and belief in, them to their Celtic and Cymric subjects and neighbours? Proceeding on this theory, we have placed the Celts and Cymry next to and after the Gotho-German nations, though they are perhaps their precursors in Europe.
In his introduction to the fairies of Great Britain as a whole (though perhaps ecluding the Celts), he writes
We have already seen that the Anglo-Saxon conquerors of Britain had in their language the terms from which are derived Elf and Dwarf, and the inference is natural that their ideas respecting these beings corresponded with those of the Scandinavians and Germans. The same may be said. of the Picts, who, akin to the Scandinavians, early seized on the Scottish Lowlands. We therefore close our survey of the Fairy Mythology of the Gotho-German race with Great Britain.
So there are quite a few parallels between Norse elves and Celtic fairies:
- The elves are akin to the ellyllon
- The dwarves and trolls are akin to the coblynau
- The nisses are akin to the bwbachod
- The necks, men and mermaids are akin to the gwragedd annwn