A thread is a CPU's state of execution as it processes a set of instructions (also referred to as a task). An interrupt is a condition that causes the CPU to store the state of its current thread of execution to begin a more important task, or to begin or resume the next task in a list of tasks. An interrupt handler is the set of CPU instructions associated with any given interrupt (a PC has several types of interrupts).
The confusing part is the fact that the thread of execution in an interrupt handler is often referred to as an interrupt.
In short, a thread is a task and an interrupt is a signal used to queue a more important task.