Martingale is a "gambling stategy" that means that you double the money after each loss. In trading it has been adapted to increased lot size (not necessary doubled lot size) instead of using a StopLoss, where a new position is opened in the same direction as the first one. Martingale-strategy can be used in different ways, but it's not correct to call all strategies that increases lot sizes as "Martingale strategies", but all trading strategies that opens new positions "IN THE SAME DIRECTION" and with "LARGER AND LARGER" lot sizes, are regarded as Martingale strategies when it comes to trading.

Grid-strategies is a strategy where 2nd,. 3rd, 4th, etc positions are NOT opened depending on any technical or fundamental analysis, but when the price has moved a specific number of pips, which is called a "PIP RANGE". This "pip range" is usually the same, but not necessarily. The important thing is that the pip-range is pre-defined and static. The calculation can be dynamic though, based on average range or something else, but in most cases, grid-strategies uses the same fix pip-range. And most such strategies also opens the first initial position based at one or more technical indicators.

Grid- and Martingale strategies are often combined, and "Grid-Martingale Strategies" have become the most popular among all strategies, not because they are better than other strategies, but because they are so easy to construct, and they usually work very well for some time (with emphase on "for some time"). The problem is, that such strategies cannot work forever, simply because sooner or later a long-lasting trend starts, which is against all the positions that are opened, so the account will loose all or almost the money. Most commercial EA's that have been marketed during the years are in fact grid-martingale strategies.