Essentially the answer is that thinking of both of these events simply in terms of 'England' and 'Scotland' is not the full picture. This answer might get slightly long-winded (what can I say, I'm quarantined!), but hopefully I can help.

Firstly, to simplify things somewhat, James I was crowned king of England primarily because he was a Protestant. However, the sort of Protestantism he felt most sympathy towards personally was not, somewhat paradoxically, really the form that was most prevalent in Scotland.

Both England and Scotland had undergone Reformations in the 16th century, but while England's Reformation had centred around the monarch and generally speaking, served to increase royal power, this was not the case in Scotland. In Scotland, the Presbyterian system of Protestantism which had emerged from their Reformation did the opposite, empowering their church and nobility and providing a body of 'resistance theory', about how the monarch could be resisted, by force where necessary.

This meant that James, and later his son Charles, would make various efforts to bring Scotland closer to England, particularly where it came to religion, which underpinned Scotland's 'limited monarchy'. This came to a head in 1638 where Charles's efforts to impose English religion on Scotland resulted in the Scots creating a 'National Covenant' and power in Scotland being seized by what was essentially a revolutionary Presbyterian government.

This government would fight both for and against Charles over the course of the Civil Wars. In 1643 it agreed a 'Solemn League and Covenant' with the English Parliament, which many saw as a stepping stone to unifying England and Scotland in both politics and religion. The Scots sent an army to England, and this was crucial in winning the 'First Civil War' for Parliament. However, when it appeared that the Parliamentarians would not keep their end of the bargain, King Charles signed the Solemn League and Covenant, and the Scots (or rather a faction of them known as 'the Engagers') fought for him in the 'Second Civil War'. Charles and the Scots lost, and he was executed. The Scots then agreed the SLC again with his son Charles II, but lost again, ultimately being defeated by Cromwell in the 'Third Civil War'.

The upshot of this is that the relationship between England and Scotland in the mid-17th century was very complicated. Some saw large parts of the Civil Wars essentially as Anglo-Scottish wars, but in reality they were more complex than that. Also while both Charles I and II fought with the Scottish Covenanters, neither really liked them much, as they felt used by them and the 'High Anglican' Protestantism favoured by both Charles and his son was completely at odds with the Presbyterianism of the Covenanters.

Now, its also important to point out that when I refer to the 'Scots' here, I am referring to the Presbyterian lowlanders who dominated Scottish politics in the 17th century. These are not, as a rule, the 'Scots' who fought with Charles Edward Stuart at Culloden. The Jacobite army at Culloden was composed of a mix of Catholic Highlanders, and Episcopalians from the east of the country (Protestants who supported bishops, as opposed to Presbyterians who did not). I will attempt in my next answer to explain why these groups supported the Jacobite rebellion in 1745.