Question
You have read about user mode and kernel mode. Are they the different from userspace and kernel space respectively?
Answer
Yes. User space is not the same as user mode. Kernel space is not the same as kernel mode.
"Modern processor architectures typically allow the CPU to operate in at least two different modes: user mode and kernel mode (sometimes also referred to as supervisor mode)." Taken from page 23 of The Linux Programming Interface by Michael Kerrisk.
User space is defined here: What Is User Space and Is It Different from the User Stack?
Kernel space is defined here: What Is Kernel Space and Is It Different from the Kernel Stack?