The period from the fourth century onwards saw both Welsh and Cornish states, but never – in the record we have, anyway – a Welsh-Cornish state. The short answer to your question is that the Cornish state was known as Dumnonia, while the most powerful Welsh state was usually Gwynedd (which combined highly defensible mountain territory with the agricultural wealth of lowland Anglesey). But, hey, this is AskHistorians! Welcome to the long answer.

First: we're covering a pretty long and pretty poorly-evidenced period here – Cornwall seems to have lain at the heart of an independent polity from some time after 350 till at least 830, while the last independent Welsh polity was not subdued by England until 1282, so there was plenty of time for rulers and states to rise and fall. But to summarise the position briefly: for most of this period Wales comprised a minimum of three different polities, Deheubarth (southern); Powys (central) and Gwynedd (northern), each of which in turn dominated a number of smaller petty kingdoms. In some periods – for example during the reigns of Maelgwyn Gwynedd in the early 6th century, Rhodri Mawr in the 850s-870s, Hywel Dda in the 940s, Llywelyn the Great in the early 13th century, and Llywelyn the Last during the 1260s-1280s – one ruler had sufficient power to control, to a greater or lesser extent, most of Wales. Several of these rulers, moreover, led alliances of men drawn from a number of different British states against Saxon or Scandinavian armies. However, Welsh territory was never formally unified under a single leader, and while some of these rulers were accorded the title "King of the Britons" (or, later on, "Prince of Wales") by chroniclers, and in some cases were powerful enough to claim some control over, or offer some protection to, other British peoples, Welsh rulers pretty much always seem to have looked north, to another British polity known as the Kingdom of Strathclyde, rather than southwards to Cornwall.

The only significant exception to this statement may have been Cadwallon ap Cadfan of Gwynedd (fl.620s). Geoffrey of Monmouth has him campaigning in Cornwall and defeating Saxon forces there. However, Geoffrey was writing in the early 12th century, and his history is notorious for its inaccuracies and inventions (he is one of the main early sources for Arthurian legend), so it's very far from clear that any such a campaign actually occurred.

Meanwhile the Britons of the south-western peninsula called their state Dumnonia, and at its peak it extended as far north as what is now Somerset and had close links with an identically-named state in Brittany. I wrote about Dumnonian history in an earlier post that you might like to check out here:

What do we know about the political situation or Rulers in Cornwall in the 700s-800s AD?

But while the Welsh rulers looked, for the most part, north, if Dumnonia's political reach ever did extend outside these borders, it would have been to the south.

Very frustratingly, we simply lack sufficient evidence to reach any firm conclusions in this respect. But, certainly, senior British churchmen – most notably St. Gildas – were active on both sides of the Channel, and it's possible (but, again, uncertain, thanks to the paucity of sources) that at some points the Cornish and Breton states had rulers in common.

I summarised the debate as to the independence, or interdependence, of Cornwall and Brittany briefly elsewhere (link at the foot of this post), in an essay about a long-remembered Breton ruler known as Conomor the Cursed, and the situation looked as follows:

Nobody doubts that the Britons of this period sailed south to establish themselves in Brittany. Close connections were undoubtedly maintained across what we now know as the English Channel; a glance at a map [of 6th century British kingdoms] shows a couple of examples of the fascinating and widespread duplication of place-names (Dumnonia/Dumnonia; Cornwall/Cornouaille) that exists between south-west England and the Breton peninsula. What is far less certain is whether the leaders who travelled to Brittany from the fourth century onwards left their lands in Britain behind – or whether there were rulers active and powerful enough to reign on both sides of the water.

In attempting to tackle this problem, we need to point, first, to the reasons for British emigration in this period. Abandoned by the Rome, and then confronted by Anglo-Saxon migration in the years 450-550, the Celtic inhabitants of Britain continued to rule in the far west, where the land was higher, rougher and more inaccessible, and where much of the soil was so poor that the invaders had little motive to press for further conquests. In consequence, British kingdoms continued to exist to the north (in Strathclyde, with its capital at Dumbarton – which means “the fortress of the Britons” –  c.450-c.1030); in Wales; and to the south, in Devon and Cornwall, where the state known as Dumnonia was certainly in existence well before 550 and survived as late as about 839.

But if a key factor in the existence of these states was geography, the same features that allowed the Celts to retain their independence also caused them serious difficulties. There was little decent land available in the highlands, and Celtic law prescribed the division of each father’s possessions among all his sons. In such circumstances, the progressive dividing up of patrimonies inevitably produced poverty and encouraged the Britons of both Cornwall and South Wales to look hungrily over the Channel for land. It is generally supposed that this emigration began no later than 350, and we know there was enough of it for a “bishop of the Britons” to have travelled from Brittany to attend the Council of Tours, which was held in 461, and for the Brythonic and Breton languages to remain indistinguishable as late as the 10th century. Small states controlled by rulers with British names existed in the Breton peninsula after 500, and in the course of the sixth century enough Britons emigrated to France, with sufficient success, for a clearly independent collection of Breton polities, with their own language and distinct identity, to have emerged a century later.

All this certainly suggests something much more interesting than the emigration of some scattered families, but it is not enough to prove that the Britons who sailed south were politically significant or that they retained lands and power in their homeland. There are, indeed, reasons to suppose that this was not the case; educated guesswork suggests that British control in Brittany was far stronger in the countryside than in its towns, where Roman and Frankish influences still predominated in this period. That, and the fact that no identifiable British “high king” emerged south of the Channel in the sixth century, argue against the existence of a ruler powerful enough to control significant territory in both Cornwall and Brittany. 

On the other hand:

Dumnonia was easily the biggest of the British kingdoms that survived the westward push of the Saxons – at its height it was something like 125 miles (200km) from end to end, making it among the largest states, by area, in all of Britain at this time. That suggests rulers of some prominence, and a degree of organisation that might have been sufficient to permit projections of their power. Conomor’s name – “Hound of the Sea” – and the powerful traditions of the Breton saints’ lives, which present him as an “unjust and unprincipled stranger” – an outsider, in other words – both suggest a possible origin in Dumnonia as well.

The most interesting fragment of evidence, though, comes from the Life of St Paul Aurelian – a much later source, remember, completed in 884, and thus one that must be treated with great caution. This mentions a “King Marcus whom by another name they call Quonomorius” – and this extract has been taken as a reference to the semi-legendary King Mark of Cornwall who figures prominently in medieval Arthurian romance and plays an especially important part in the story of Tristan and Yseult (that is, Tristan and Isolde). In this romance, Mark is a king of Cornwall – Dumnonia – and Tristan is his nephew, sent to Ireland to bring back Mark’s beautiful young bride, who instead, inevitably, falls in love with the girl himself.