Does it mean that it won't be a steady income of BTC like it is now with ETH/other altcoin mining or is the income going to be steady but depending on hash rate and network difficulty?
The income is never really steady. In time more and more people will mine and the miner hardware improve too.
So you should expect your income to slowly decrease in time.
There are a ton of machines, each and every one sending tons of hashes every second. Then one such hash wins and gets the reward (which will get split by the pool between its users). Now the competition sounds clearer? Now imagine that tomorrow somebody in the world starts 1000 more ASICs. Will your chances get affected? (And all this means, shortly, that the difficulty affects your income)