Not really. The War of the Roses was known at the time and for more than a century thereafter as the Civil Wars, but it has little in common with what we know as the English Civil War today.

The War of the Roses (1455-1487) was a series of conflicts over control of the English throne between the two cadet branches of the royal House of Plantagenet: Lancaster and York. Its roots lie in the wake of the Hundred Years' War (1337-1453) between England and France and its emergent economic and political troubles (e.g. financial hardship, weakening of the monarchy, etc.), and was further fueled by the rivaling houses' gamble for power.

The war itself was fought on the grounds of and was perceived as a calculated attempt by the rivaling dynasties to usurp the English Crown. Ultimately, it was just another noble feud that happened by the dozens throughout medieval Europe and was in no way unique.

On the other hand, the English Civil War (1642-1651) was indeed quite unique and very different in nature. As one of the theatres of the War of Three Kingdoms, it was an intertwined conflict fought over ideological resentments of religion and governance - which distinguishes the casus belli. The war was lead between Protestants and Irish Catholics, with the latter fighting against systemic discrimination of their denomination, as well as between the different factions of Prostestantism (e.g. Anglicans, Puritans, Presbyterians). The main cause of the war, however, was the question of the King's rule.

Unlike other European countries like France or Spain, England had never been an absolute monarchy. As early as 1215, nobility and clergy had consolidated their privileges with the signing of the Magna Charta, which had constrained the royal prerogatives ever since. Inspired by the doctrines of absolutism and divine right, King James VI & I and King Charles I, nevertheless, attempted to strengthen their personal rule and increasingly ignored the concerns of Parliament in the early 17th century.

When Charles I ascended to the throne in 1625 (in an already heated atmosphere of mutual distrust and suspicion), he came under increasing scrutiny of a mostly Protestant Parliament for his marriage to Catholic Princess Henrietta Maria, his religious policies - which many Puritans condemned as 'too Catholic' - and his failed military intervention in France to aide the Huguenots. Exasperated at Parliament's constant scrutiny and interference, Charles dissolved it in 1629 and ruled without any parliament for eleven years. In sight of the Scottish rebellion and in need of new funds, he was forced to recall Parliament in 1640, which proved even more hostile to him and his policies than its predecessor. When his attempt to arrest five leading members of the opposition failed in 1642, civil war finally broke out between his Royalist supporters and Parlamentarians. The war ended with the capture of Charles, his execution in 1649 and the abolition of the monarchy.

Although the monarchy was eventually restored in 1660, it was still only with the consent of Parliament. So the English Civil War effectively set England and Scotland on course towards a parliamentary monarchy type of government - a development cemented by the Glorious Revolution in 1688. The political and ideological ramifications of the Civil War were very transformational, whereas the War of the Roses was a mere gamble for power.