I have read about the next upcoming fork planned for the block 1788000 (around the 9th of March). After that block, will I need to update the Monero daemon, the wallet, or both? And what about the miner programs?
Thanks in advance for answers.
Yes, as we have done before for the other forks, you'll need to update daemon, wallet, and miner.
As you can see here, the upcoming fork will bring to Monero a new PoW algorithm: the CNv4, Cryptonight variant 4 aka CryptonightR.