Can someone explain woofers to me in this case?.. soundbars

when reproducing sound, it takes far more power to produce low frequency audio than it does for mid's and higher frerquencies. One of the main uses for a powered subwoofer is to take the load off the system amplifiers for the low frequencies and handle them with the sub's built in amplifier. This lets the audio system amplifiers work more efficiently in the mid and upper frequency range.

I don't know how the Mitsbu handles low frequencies, but a typical soundbar really needs some assistance with lower frequencies because tiny speakers just cannot reproduce sounds effectively below 150Hz or so.

at 4.375" in diameter, they are not woofers...too small, so they are probably mid-range speakers.

Technically, anything that is not a tweeter is a woofer. There is such a thing as a hybrid cone(sorry don't know the technical term for it) that allows a single woofer to have a tweeter element built into it so that it can power both to have a larger frequency range in a smaller package. Many $150-$400 speakers systems use the hybrids. I believe the Mitsu and the YSP "Beam Drivers" both use hybrid cones. At least that is what I can tell form pictures.
As for the YSP vs the Mistu TV, the difference is in the total frequency range it has. The Mitsu TV has many small micro-sized speakers so that some can be dedicated to different fequency ranges so they have less work to do. Also to be able to produce a louder sound through redundancy.
The Yamaha will be able to produce mid's while the Mitsu will never be able to. That is the only real difference. You need larger woofers with more power to be able to produce low frequencies. Neither will be able to produce anything considered as Low end frequencies.