Resistance is the opposition of electron flow (i.e. current) through a device in a circuit. In the water analogy, it’s a constriction in the pipe that prevents water from flowing and reduces the flow rate (analogous to electrical current). If you increase the water pressure (analogous to a voltage), more water will flow through the constriction (increased current), but more energy is required by the pump that creates the water pressure in order to overcome the resistriction in the pipe. So, the resistance is theoretically constant while the amount of water flowing will depend on the pressure, and more energy is required to increase the amount of water through the resistricted pipe.
Load is the amount of electrical power (both voltage and current) that a device consumes to perform work, like a motor, pump, or light bulb. The water analogy kinda breaks down here. Suppose you have a pressure-activated switch spliced into the pipe. Both water pressure and water flow are needed to trigger the switch. If the pressure is too low, the switch will not be activated. Similarly, if there is too little water flowing through the pipe to the switch, the switch will not activate because there is not enough energy to trigger the switch.
The difference is subtle, but load includes the power (closely related to electrical energy) needed to overcome the resistance. To make matters more confusing, the load is often represented as a resistor in a circuit diagram.
A worn out motor will draw more current at a given voltage because electrical energy is being wasted, such as overcoming friction from a worn out bearing in a motor or oxidation on the electrical connections that inceases resistance and generates heat. If the power source cannot supply enough energy to the motor, the motor will spin slower or not at all. Likewise, if a large power source is connected to a jammed motor, current will flow although it cannot rotate, but it will generate a lot of heat in the process.
Batteries are power sources that have limitations with respect to both current and voltage. The voltage is dependent on the number of electrochemical cells that are wired together in series, and each cell’s voltage is dependent on the 2 materials and the chemical reaction between those 2 materials that generates electricity. The current is limited by the size of the cell, or the amount of chemicals that can generate flowing electrons at the cell voltage.
If the load is increased within a circuit, like increasing the radio’s volume while the ignition is off, the battery will have to supply more energy to the amplifier and speakers within the audio system. So, more of the chemical reagents have to react in order to keep up with the electrical demand, and the battery has to work “harder”. Also, the battery will have internal losses from undesirable side-reactions and the effect of entropy when the electrical demand is higher.
I hope that helps.