Generally, the difference between a system and a tool is that a system is a customized environment which processes the inputs and the processed materials are our outputs. But a software tools -as it seems- is a tool which can be used in other systems to help them in achieving their goals. DMTs are tools that can be used to make a DSS or simply can be used in a system for some reports.
Decision support systems are helpful for middle level executives to make decisions. However, Decision making tools are for every one in organization to make decision.
Decision Support Systems (DSS) comprise components like models base, data base and interfaces that allow communication between the user (Decision Maker) and components of the system. Many of the DSS components can be also described as decision making tools (like models, optimization procedures, etc.). I would not say that DSS represents the "software or IT package" containing one or more decision making tools. I would rather say, that DSS contains software that represents one or more decision making tools. The most important element of the DSS is an interface that allows user to "manipulate" these tools, analyze various alternatives or policies which then are to be evaluated by the human involved in decision making process.
Let me try and add some insight in addition to what others have provided above ...
A distinction between "tools" and "systems" is that "tools" usually refers to the hardware/software infrastructure used to create an (IT) "system" of some kind. For example MS Excel on a Windows machine comprises a "tool." A specific spreadsheet application built using that tool for financial what-if analysis is a Decision Support SYstem built using that tool.
That said, a distinction between Decision Support Systems (DSS) and Decision Making Systems (DMS) is that the former supports a human decision maker in some decision-making tasks whereas the latter also assumes the role of decision making. An oft used example to illustrate this distinction is that whereas the Financial What-If Analysis tool in the example above is a DSS (it allows the decision maker (DM) to explore alternatives, but the DM makes the final decision based on such analysis), an Expert System (ES) that does such exploration and also makes a recommendation would be a Decision Making System.
Assuming that by Decision Making Tools, you mean Decision Making Systems, one may also visualize that a complex DSS may itself, embody within it one or more ESs. For example, a non-expert human may consult a human expert for advice but he/she remains the final decision maker. So also, a DSS may be comprised of one or more DMSs.
Likewise, a DMS may contain within it one or more DSSs. Going to the spreadsheet Financial What-If Analysis system, such a system may provide inputs to a rule-based expert system that takes the output from the What-If Analysis component to arrive at a judgment call on a course of action.
The ultimate distinction in whether one would regard the comprehensive system as being a DMS or a DSS is based on who makes the final judgement -- does the machine also make decisions or does it merely provide the fodder for making decisions?
One may envisage that DMSs are successful only in very narrow, well-defined, well-structured settings (a simple example, your thermostat decised whether or not your aircon must kick in based on ambient temperature conditions it senses). In all other cases, the systems act as DSSs.
Decision Support Systems (DSS) in business use (1) Analytical models, (2) specialized databases, (3) a decision maker’s own insights and judgments, and (4) an interactive, computer-based modeling process to support semi-structured business decisions. While Decision Making Tools (DMT) are for organizing information in transparent ways so that decision makers can understand the ramifications of their actions, regardless of the ultimate decision criterion they employ in choosing an action. Therefore DSS is a bigger entity which houses DMTs