There are eight different types of card rarities in Battle Spirits.
Commons (コモン) are indicated on the bottom of a card with a small "C". As the name implies, they are the most common rarity in the trading card game, taking up the majority of a single set. Common Spirits usually have a low cost and have few effects. They usually have no foil patterns.
Uncommons (アンコモン) are indicated on the bottom of a card with a small "U". Starting from SD33, Uncommon cards no longer exist. During their lifespan, there were generally one or two Uncommons per pack, and packs without a rare had an Uncommon as the last card instead. Uncommons replacing a rare may have a slight foil on them. Similar to Commons, Uncommons usually have only a mediocre effect.
Rares (レア) are indicated on the bottom of a card with a small "R". Like the name suggests, Rares are rarer than Commons and Uncomons, although not as rare as Master Rares and X-Rares. In a single booster pack, there is only one rare card, located in the last slot of a booster pack, although it can be replaced with an uncommon card or a card with higher rarity. Starting in SD10, Rare Spirits have full arts that cover most of the card, but the bottom half is mostly obscured by a white text box. Rare cards usually have stronger effects. Save for the text box, Rares are completely foil.
Master Rares (マスターレア) are indicated on the bottom of a card with a small "M". Master Rares are rarer than regular Rares but slightly more common than X-Rares. In most sets, there is only one Master Rare for every color. In a regular booster box, there are only about three Master Rares. Originally, Master Rare Spirits did not have full arts, although the whole card, including the text box, was foil. Starting in SD10, Master Rare Spirits have full arts and lack a card stamp in the middle.
X-Rares (Xレア) are indicated on the bottom of a card with a small "X". X-Rares are the second rarest cards in booster packs, falling only to XX-Rares. Generally, there is at least one X-Rare in a set for each color. In a single booster box, there are usually about two to three X-Rares. Aside from some campaign X-Rares, there are only X-Rare Spirits, Braves, and Ultimates.
X-Rare cards lack the card type symbol in the text box, and instead have a stylized "X" stamp. X-Rares have a special textured foil pattern on them, and starting from SD10, they have a special full art that extends beyond the card borders.
XX-Rares (XXレア), introduced in BS31, are indicated on the bottom of a card with a small "XX". XX-Rares are the rarest cards that can be found in a booster pack, being so rare that a single booster box may not even contain one. There are usually only 2 XX-Rares per set. XX-Rares are only either Spirits or Ultimates. XX-Rares are all full art, but unlike X-Rares, they also have a special card border and a golden background.
Mythic X-Rares are an extremely rare type of cards. There is only one Mythic X-Rare, The AbsoluteDragonDeity Amaterasu-Dragon, and only three copies of it exist. Appearance-wise, they differ drastically from other cards, to the point where even the effects are in a different font. They have extremely powerful effects.
Promotional Cards (プロモーションカード) are cards that aren't part of any booster set or starter deck. Promo cards can be obtained in various ways, including magazines and participation in Shop Battles and other special events. Occasionally, Promo cards are also of X-Rare rarity, but unlike X-Rares, aren't engraved with a pattern.
Another type of Promo cards, Campaign Cards, were introduced in BS18. Despite not being part of the main set, they can be found in booster packs, the same way one would expect to find rarer cards. Most campaign cards are also X-Rares.