It is said that medium-chain triglycerides can be converted “more easily” to ketones in the body, but I have no idea what that means or what study(ies) that is based on. Since ketones are partially-metabolised fatty acids, I’m not sure that it makes that much difference. As far as I know, the mitochondria simply carve a certain number of carbon atoms off the chain and then go to work, repeating the cycle until the entire chain has been carved up.
As for whether the mitochondrion stops the metabolic process at one or more of the ketone bodies, or whether it continues metabolising till it’s left with carbon dioxide and water, that depends on a number of different stimuli. Skeletal muscle cells prefer to start with fatty acids and metabolise them completely, the liver makes ketones and ships them out in the blood stream for whatever other organs want them, and the heart and brain start with ketones and metabolise them fully.
Any cell that can metabolise fatty acids produces ketones during that process, but it doesn’t usually stop metabolising at that point. Only the liver makes quantities of ketones to be shared, so far as I know.
The process of producing ketones from a fat is analogous to the production of charcoal from burning wood. Most stoves just go all the way to ash and carbon dioxide, unless someone intervenes and saves the charcoal once the wood has been partially burnt.