Bitcoin dominance is covered in full in the entry Dominance, which gives the formula, the history of the measure and how traders use it. This page gives a short definition and explains the different names.
Bitcoin dominance is the market capitalization of Bitcoin divided by the combined market capitalization of all tracked cryptocurrencies, expressed as a percentage. A rising figure means bitcoin is gaining value relative to the rest of the market, while a falling figure means altcoins are gaining ground. Because data providers track different sets of coins, and some exclude stablecoins, their dominance figures can differ by several percentage points at the same moment.
"BTCD" is the ticker-style code used on charting platforms that publish the figure as a tradable-looking chart, and "BTC.D" is a common variant. Plain "dominance" is the general term, since the same calculation can be applied to ether, stablecoins or any other asset. All of these names describe the same measure, which is a market statistic rather than a coin or token in its own right.