The award system of the SCA can be confusing to new members, or even people who've been around for a while. Here's a quick primer of some of the broad aspects.
Everyone who participates in the society is assumed to be a gentleman or lady. Even the newest member should be treated courteously, and addressed as milord or milady. More formally, they are not styled with a title of any kind until they receive formal recognition from the kingdom in the form of arms (arms also refers to the heraldic design chosen by the participant).
The right to bear arms and be addressed with a title of one's own is given by the king and queen in a court. (Or by someone acting on their behalf and at their direction, usually a prince and/or princess or a landed baron/baroness, but very occasionally by someone else in a "regency court" - this would almost certainly be a royal peer specifically delegated to give the award on their majesties' behalf.)
Arms are given in three ways, each conveying a different type of rank.
1. Arms are first given by award. An award of arms, given throughout the SCA, conveys this basic status. One is an armiger after being awarded arms. In addition to an award of arms, each kingdom has a set of other awards which convey armigerous status. In the Middle Kingdom, for example, one may receive the Award of the Purple Fret or the Award of the Dragon's Tooth. This is both an independent distinction and also conveys armigerous status if it was not given before in a "bare" award of arms. Anyone with any such award is addressed as Lord John Doe or Lady Jane Roe (first names only - one is Lord John Doe, not Lord Doe.)
2. Arms are next given by grant. A grant of arms is given in different ways in the different kingdoms. In the MidRealm, it is given as a "bare" award, a GoA, only to kingdom officers (except for a brief period in the 1990s). In the Middle, one is granted arms together with membership in an order, such the Order of the Greenwood Company or the Order of the Dragon's Heart. This is a relatively new concept in the Middle - this arrangement dates only from a 2000 reorganization of the awards system here. It is a fairly big deal to be made a "companion" of one of these orders, and a very exclusive type of honor to have a "bare" GoA. Anyone with granted arms is addressed as The Honorable Lord John Doe or The Honorable Lady Jane Roe (again, not Lord Doe). For this level of rank, it is also appropriate for others to refer to such a person as His Lordship John Doe or Her Ladyship Jane Roe (one would not commonly refer to oneself this way). With granted arms, one still answers to Lord or Lady, too, and it is common to use THL Jane Roe for short, too.
3. Finally, arms may be given by patent. This is the highest form of honor conveyed in SCA courts. It is given only in association with the SCA-wide peerage orders - the Order of the Chivalry, the Order of the Laurel, the Order of the Pelican and the Order of the Rose, and with the titles of Count/ess and Duke/Duchess. One is said to be a peer at this level of recognition. A member of the Chivalry is either Sir John Doe or Dame Jane Roe (actually, almost all lady knights prefer Sir, as well); other peers are Master John Doe or Mistress Jane Roe (again, not Master Doe). (A wrinkle here - some members of the Chivalry prefer to style themselves Masters or Mistresses - this is prearranged for those whose religion or personal philosophy prevent their swearing an oath of fealty, as knights are required to do.) Royal peers, by the way, are those who have served once as king or queen and are made a count or countess; or twice or more and are made a duke or duchess.
So, same arms, and the arms given is the design that the recipient has chosen for him- or herself and registered with the College of Arms. But a different rank for each level.
More about awards and heraldry tomorrow. For more detail, by the way, see Master Thorvald's Middle Kingdom Awards page.
Correction: When I say above that the Order of the Rose is a peerage order, that isn't quite right. At present in the Middle Kingdom, it is an order which conveys no precedence. It is SCA-wide, it does convey a peerage in some kingdoms, and it used to here.