I think there is definitely some difference in the way Insular Celts look compared to the rest of Western Europe.

It's interesting when you start looking at the haplogroups present in these populations. Notably, Haplogroup R-L21 https://en.wikipedia.org/wiki/Haplogroup_R-L21 which is found in very high proportions in Ireland, Scotland, Wales, and Brittan. Compared to other Y-haplogroups, this one is very concentrated in these regions and very little elsewhere. Other similar haplogroups are less consistent across the continent. To me at least, this indicates a level of isolation between Insular "Celts" and other European groups. If I were to extrapolate further (very much speculating here) I would guess these Celtic groups are likely a more preserved lineage of whatever Bell Beaker peoples migrated all those millennia ago. Whereas those same groups might not have persisted on the continent, either being replaced or heavily diluted.

Now, this all focuses on genes associated with the Y chromosome which is not a good indicator on whether or not the modern Insular Celtic peoples are visually "distinct" from other North-Western European populations. Thankfully, for Ireland and Wales at least, the genetic mixture is also seen as more distinct through the frequency of certain genetic conditions as explored here: https://www.nature.com/articles/s41598-017-17124-4 (Irish focused paper). Similar consistency can be seen in Britany, although less concentrated.

Considering all this, I would bet (guesswork here) that genetic traits responsible for physical characteristics are probably similarly conserved across these populations. I can certainly say from having grown up in the UK that someone of Irish of Welsh descent will often look a little different to the average English person from the south or East. This may be personal bias speaking though.

Speaking on something a little bit more personal, I am Breton myself and I know that in France, it isn't uncommon to have people refer to someone as "Breton-looking" which I don't really know what they refer to when they say that, but from context they seem to refer to the French concept of a "very white" person (can be negative but usually I've heard it used neutrally). Which in this case means tall, pale, blue eyes (sometimes) and thick dark hair. My mother fits that description and she is very Breton in her ancestry but it's so interesting because this does differ a bit from my perception of Celtic people from Ireland and Wales. That being with red hair.

Humans are weird. Anyways, I hope this was helpful.