The rank of admiral originally referred to anyone who had command authority of a group of ships. Merchant ships in Elizabethan times, for example, would elect an "admiral" when sailing in convoy, although his ability to command individual ships depended entirely on his persuasive skills. There was no official authority.

Later, admirals could be appointed to command parts of a fleet or different divisions of a fleet; during the fight against the Spanish Armada, for example, Lord Howard was admiral and Drake vice-admiral, with Sir John Hawkins as rear-admiral; but this was not intended to be a permanent rank, rather an ad hoc arrangement for that series of engagements. (Captaincy and the like was also not a permanent rank at this time, but I'm drifting off topic.)

So to get to part of your question, at least in the English tradition there were three types of admiral: admiral, vice-admiral and rear-admiral, in that order of seniority; above all of them stood a single Admiral of the Fleet. In the English navy, let's say around Samuel Pepys' time, the fleet was divided into three squadrons (red, white and blue) and each squadron had an admiral, vice-admiral and rear admiral, and the squadrons and ranks each had seniority. (In other words, the red squadron was the most senior, followed by the white and blue; a man would attain the rank of rear-admiral of the blue, then white, then red; then vice-admiral of the blue, etc.) We get the first official seniority lists around 1691. To quote myself from a previous answer:

The major upheaval that the English navy had dealt with after 1689 was the complete collapse of the authority of the Admiralty. William III of England (William II of Scotland) thought of it as a dependency of Parliament, as the Dutch navies were to the States-General, and not as the independent agency it had been previously. (William, of course, had been born William, Prince of Orange, and raised in the Dutch court.) So the Navy in this period became a proxy for the power struggle between William and Parliament; we get oddities such as the crown asking in 1698 for 10,000 seamen and 3,000 Marines and Parliament voting funds for 15,000 sailors and no Marines. As a result of the decline of real authority by the Admiralty, the Navy Board grew in power and often made major decisions without consulting anyone in particular, including the sovereign, and tended to be inflexible in the face of even reasonable requests from captains. At the same time, related boards that had relationships with the navy (the Ordnance Board, Transport Board, Prize Commission, various medical boards) did not work together. The decline of the Admiralty meant that no consolidated naval budgets were ever presented to Parliament or persons who could make decisions about funding. This lead to chronic under-funding or funding out of whack with actual needs. This funding crisis was not unique to the navy; the credit collapse of the Bank of England in 1697 was caused at least partly by the imbalance of long-term debt to actual revenues, and it eventually helped prompt long-term reforms such as "funded" long-term debt in the early 16th century.

This same period saw changes in how the officer corps was organized, and moved toward the model that we saw leading up to the Napoleonic wars and continuing on it. Between 1690 and 1701, the growth of the Navy meant that almost 50 percent more men were needed to comprise a full complement of commissioned officers, which meant that organization had to be created where there was little before. In 1691 we get the first official seniority list, and in 1694 a schedule of half-pay was introduced for unemployed officers (before this, officers would be paid off at the end of a voyage, and unless given a new one would have to seek employment elsewhere). In 1713, the navy clarified this to grant half-pay to captains and lieutenants who "stand fair to be employed when there will be an occasion" (N.A.M. Rodger, Command of the Ocean, pp. 203). During this period, though, there was not a rigid distinction between post-ships (those allowed a post-captain) and others, and captains could be lieutenants, lieutenants could be gunners (later warrant officers), etc. This would not be resolved until later in the century.

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A major innovation during the Seven Years' War (1754-63) was the creation of the divisional system, which was popularized (and maybe invented by) Vice-Admiral Thomas Smith. The system divided a ship's company into divisions allocated to lieutenants and warrant officers, who would be directly responsible for the men under their command. This had the effect of making sure that even in the largest ships, men would be known to at least one officer. That relationship was crucial in creating humane relations that were essential to discipline.

There were several changes to officers' ranks and career structure during this period as well. To start with, officers became fixed in ranks (rather than having a lieutenant serve as a commander of a ship, for example, he would only command a certain size of ship as a master and commander or post-captain, and that rank would be fixed upon promotion).

Secondarily, in 1743 George II agreed to expand the number of admirals from 10 to 21: there could now be more than one in each rank. Before this, admirals were by convention divided into red, white and blue squadron, commanded by an Admiral of the Fleet, each seen as a distinct rank and promotion only by seniority. By 1747, though, the Navy had one Admiral of the Fleet, six admirals, six vice-admirals and eight rear-admirals. Even with that expansion in rank, there weren't enough admirals for all commands, and there was still no way to promote men to admiral from the captain's list; seniority was the only step. So by 1747 a rank of admiral "without distinction of colours" was created for the specific purpose of superannuating men into a non-active rank, which allowed the Navy to reach further into the captains' ranks to promote.

The whole structure of the Navy was controlled by an interconnected set of boards (Transport, Ordnance, Sick and Hurt, Victualling and others at different periods), run by an overall Admiralty with a civilian First Lord.

This might help -- does it clarify your question at all? (Obviously I'm speaking of the English and British navy, which is what I have some expertise in.)