Trademark rights are limited to the goods or services for which your trademark is registered. While you may have exclusive rights over your mark for certain goods or services, another company may legitimately use the same trademark for goods or services which are not similar.
For example, you may have a trademark FOREVER GREENY for garden tools and another company may register a trademark for FOREVER GREENY for mining software or gas station. As the industries are unrelated, there is no confusion so mark can co-exist.
Most countries follow the system of International Classification of Goods and Services which divides goods into 34 classes and services into 11 classes.
You may apply to register your trademark in more than one class.
Please note that some countries require separate applications for each class of goods or services (Mexico is a notable example).