They are all honorary positions in the Papal Household. They are usually awarded to priests for their service to the Church. As no office or function is attached to them there is no difference other than their order of precedence and your list is in reverse order, i.e. protonotary apostolic is the highest grade and chaplain of His Holiness the lowest.
The grades are new following the simplification of the curial reform in 1969. The current middle grade was formerly a domestic prelate and they and protonotaries apostolic were entitled to be addressed Right Reverend Monsignor. The current grade of chaplain of His Holiness used to be called papal chamberlains and were addressed Very Reverend Monsignor. Nowadays all monsignors are styled Reverend Monsignor. Those who were made monsignori prior to the reforms and are still alive can retain the former styles of address.
A chaplain of His Holiness wears a black cassock with purple buttons and trim and a purple sash. Honorary prelates and protonotaries apostolic have a black cassock with red buttons and trim but a purple sash. Both the latter can wear a purple cassock when in choir dress. Protonotaries also have the right to the silk cape called the ferraiolo.
