Well,
RPG is basically a genre in which characters in a party assume "roles." Each character in RPGs is assigned a role, class, and each levels up - or grows - by gaining experience points. There are a variety of sub-genres that have spawned from this term, and the confusion of the OP appears to derive from the definition of what a role means [in this context]. The term RPG simply refers to the roles given in
gameplay much rather than the story itself, though this is a very important aspect, nonetheless. However, I'll be covering
gameplay aspects of a role. Action and turn-based RPGs shall be my focus as this seems to be wherein the confusion lies, given the similarities with the Adventure genre.
Roles
As stated above, each character in the party assumes a "role." How roles are assigned is usually optional to the player, and can depend on such variables as a given enemy's overall stats, what status effects it employs, its HP/MP amount, and a variety of other factors. There are games in the RPG genre in which roles are not optional, but allow for some [or a high] degree of malleability. I'll be sticking to the optional roles. The most well known "roles" in an action and turn-based RPGs are, but not restricted to:
- Tank: This role typically redirects attention away from the rest of the party onto itself in order to protect them. As such, a tank typically suffers large amounts of damage, but boasts high defense stats and HP. This role is typically strong, slow, and heavy.
- Damage dealer: A role that, as the name implies, deals damage. They typically boast higher speed stats than tanks. It can dish out damage to the enemy while its focus is on the party's tank. A damage dealer's stats are typically balanced throughout, but emphasis might be placed on Strength and/or Magic depending on which class is involved.
- Supporter: This role is responsible for supporting and/or enhancing the party in a variety of ways. Supporters heal and raise stats of the party, such as Speed, Evasiveness, Power (Strength), Defense, Magic, and Magic Defense. This role typically sports a lower damage output, lower defense, etc., but boasts HIGH magical stats. Despite it's weaknesses, it is a huge asset to the party.
The above roles must be employed both tactically and strategically in battle for a positive outcome. This means assigning the correct role to a given party member is very important, as the tide of battle depends on each role's stats and how well they operate together in battle. As such, poorly assigning roles can be highly detrimental to the battle and result in the party's demise. There are far more roles than listed above, but I stuck to the most common.
Classes
In RPGs each character in a party is assigned a class, or job (job class). Classes include such jobs as Knight, Swordsman, and White Mage. In most RPGs, each character's job is assigned automatically, and in others this is optional to the player. Each class boasts a unique set of skills, stats and abilities. Knights typically assume the role of tank. Their weapons include lances, axes, broadswords, etc. As a tank, this job might have low speed stats, but boast high defense, HP, and deals a decent amount of damage. Swordsmen usually assume the role of damage dealer, as such, they are responsible for racking up damage while the enemy's attention is directed to the tank. This job typically wields such weapons as small swords [and shields] and spears. Their stats are typically balanced throughout with emphasis placed on Strength for higher damage output. Magic for this job class can range from decent to minimal; Black Mages are damage dealers that typically boast high Magic. White mages typically assume the role of supporter. As such, they are responsible for enhancing the party's stats with status boosting magics - which boost defense, power, speed, and so forth, though temporarily. They can also heal and relieve the party from status ailments caused by a given enemy's status effects (poison, blindness, sleep, paralysis, etc.). Though, the White Mage is generally weaker as far as physical strength goes, it is a valuable asset to the party, and the success of battle can depend greatly on this job and its associated role. It is wise to evaluate each job's traits and assign the appropriate role to accentuate said traits. Keep in mind that there are more classes than I have covered above.
Experience
Another feature of RPGs is the experience point (EXP) system. Each character that participates in battle receives EXP at the battle's end. How points are given can be determined by a variety of factors including the amount of points the enemy is worth, but also how well the party performs in battle. The former involves the difficulty of the enemy, as it is usually the basis of the amount of points the party will receive. The latter is not as common, but it involves the party's performance and how efficiently strategy and tactics are used in battle. Each character "grows" as a result of gaining experience. This simply means that a character's various stats increase and more options become available, such as the ability to assign roles to a job where this was previously not possible or detrimental to the battle. For example, the White Mage job class can assume the role of tank and a knight can assume the role of support character. New abilities, equipment, weapons, etc. also become available with EXP. The possibilities become incredibly flexible.
Action RPGs may contain elements of the adventure genre and vice-versa. But as you can see, there is a clear distinction between the adventure and action/turn based RPG genres. Zelda is not an RPG - of any kind - but has featured RPG-like elements. There simply has never been enough of said elements to warrant an RPG label. Well, one could argue the amount of RPG elements Zelda II: The Adventure of Link contained. However, if anything, it'd likely be given the label of Adventure-RPG. To reiterate, what I have touched on above is merely a fraction.