Why disabling interrupts disables kernel preemption and how spin lock disables preemption

I am reading Linux Kernel Development recently, and I have a few questions related to disabling preemption.

1. In the "Interrupt Control" section of chapter 7, it says:

   Moreover, disabling interrupts also disables kernel preemption.

   I also read from the book that kernel preemption can occur in the follow cases:

   When an interrupt handler exits, before returning to kernel-space.
   When kernel code becomes preemptible again.
   If a task in the kernel explicitly calls schedule()
   If a task in ther kernel blocks (which results in a call to schedule())

   But I can't relate disabling interrupts with these cases.

2. As far as I know, a spinlock would disable preemption with the preempt_disable() function.

   The post What exactly are "spin-locks"?says:

   On a single core machine a spinlock is simply a "disable interrupts" or "raise IRQL" which prevents thread scheduling completely.

   Does preempt_disable() disable preemption by disabling interrupts?