I understand caste as inherited social status. A hereditary monarchy is a caste and so is the hereditary nobility just below it. Your caste at birth determines how you are addressed and treated; it may also determine what you can do with your life - or, more positively, it may be that some things are reserved for you. In the UK, the royal and noble castes are rooted economically in the ownership of land and residential property and they have strong military links. Young Princes of the blood still fight in colonial wars.
Class is not inherited in this way. It's determined largely by your income and wealth (from a broad sociological perspective) or more precisely by relationships of ownership and control of the means of production (from a Marxist perspective).
But wealth is passed between generations - the playing field is only levelled very occasionally by war or hyperinflation - and so too is what the sociologist Pierre Bourdieu calls cultural capital. Thus does class become hereditary, your origins determining your destination even without titles or blood lineages.
In societies like Britain's, where there is both caste and class, classes blur into castes and the castes may need to take on the character of classes. In the first case, the rich and powerful seek titles which they can pass on and seek education for their children alongside the children of the upper castes. Wealth passes from one generation to the next. The upper castes, in turn, find it necessary to engage in trade (and not just in war) to maintain their position. Every corporation has at least one Lord on its Board of Directors - and in some cases a good title (Earl or above) can still compensate for deficiency of intelligence.
So we end up with what I will call a classte system.
Even where a social group is not technically a classte, it may take on features of a classte - as it were, by osmosis. So in the UK, we have a political classte which succeeds in creating and sustaining itself out of strong family, school, occupational and club associations, strong enough to withstand the challenge of democratic elections. It also creates political cultures, like the procedures of the House of Commons, which set up barriers to challenge from interlopers. Remarkably, it has never had to face a challenge from a Beppe Grillo.