Final answer:
Territories indirectly ruled as suzerainties maintained internal autonomy but were ultimately under British Crown sovereignty, exemplified by the British East India Company's rule in India pre-British Raj and the changing policies in American colonies post-Seven Years' War.
Step-by-step explanation:
Certain territories were indirectly ruled as suzerainties; they maintained internal autonomy, but sovereignty rested with the British Crown. This meant that while local leaders had the ability to govern their territories' internal matters, they had to submit to the British Crown's authority when it came to foreign policy and overarching governance. In the context of the British Empire, this structure of control allowed the British to manage their colonies with less resistance, by reinforcing the power of local elites in exchange for cooperation with British mandates, especially in terms of taxation and military support.
In India, the British East India Company initially engaged in indirect rule, working with Indian elites who would enact the company's economic policies. However, after the suppression of the 1857 Sepoy Mutiny, the British government took direct control and established the British Raj where the British Crown had direct rule over India. Still, nominal local rulers were left in place as a façade of the previous system of indirect rule.
In the Americas, many British colonies initially enjoyed a certain degree of self-rule under the policy of salutary neglect. However, with time, and especially after the Seven Years' War, the British Crown sought to gain tighter control over its colonies, leading to discontent and eventually, the American Revolution. This transition highlights the shift from a more indirectly ruled approach to a tighter grip by the British Crown, influencing the relationships between the colonies and Britain.