Difference between fastboot and recoverymode in android

I just wants to know the difference between fastboot and recovery modes in android device.

So far my understanding I thought that

Recovery mode : contains a small Linux image, having some simple User interface with few recovery options.

fastboot mode : Once the phone is into fastboot mode we can install recovery images.

can you please confirm whether my understanding is correct or not and please tell me when to use which one or combination of these two .

• Recovery mode is small Linux operating system where you can factory reset your device or update your device with vendors images.
• Fastboot it's a tool which comes with the android sdk and you can use it to re-flash partitions of your device. Because fastboot starts before android and even when android isn't installed you can use it as an alternative of recovery mode in case recovery mode partition is corrupted. Every phone usually has fastboot,but some vendors choose to replace fastboot with their tool. Like samsung, instead of fastboot it has Odin.

Now, fastboot is more useful because you can use it as a recovery method when you don't have another recovery method.