well in a coaxal speaker a 2 way has a tweeter mounted in the middle of a woofer and a 3 way has a tweeter and mid (or sub tweeter) mounted in the middle of a woofer (no difference imo between 2 and 3 way coaxials)
in a component a 2 way has a woofer and a tweeter that are not connected and have a seperate crossover. and a 3 way has a seperate tweeter, mid range and woofer and a seperate crossover.
"3-way will give much smoother response than a 2-way."
That was disproven in the 80s. The "more ways is better" argument resulted in dismal hi-fi until better research was put into both sides of the argument and the conclusion was made that both can work equally well. There are plenty of 6.5" midbasses that will play dead-flat up to 7khz and do so better than 3 way systems can, and of course the opposite is true as well, just depends on what you're comparing.