You got it right regarding the channel count.

A send parallels the signal from the channel strip to an effects loop and is returned on the 'send return' jack. It splits the signal in other words. One is the dry signal running through the channel strip, the other through the effects send and return. You can use the send knobs on the channel strip to 'send' the original signal and vary the amount of effect used on each channel. The more sends you have on a channel strip the more effects you can wire to the board without a patchbay. These sends can also be used as a monitor output to stage monitors for musicians, or a headphone mix in the studio. On lower end boards there are not usually enough of these to use as effects sends and headphone monitors at the same time unless you're a solo musician or are recording one or two people at a time.

I was also speaking of the way Yamaha makes up their buss count. A buss is usually an out that you can assign any channel signal to, to get it out of the board as opposed to a direct out (right out of the channel strip bypassing the EQ and sends). A send is what you can use for monitor mixes or effects routing for the monitor mix and for mixdown out of the stereo buss.

A four buss board has four individual groups going out on their own outputs. You can assign any or all channels on the desk to any of these busses.

The same with an eight buss board or a twelve buss board.

Busses also allow you to combine channels into groups. An example would be the drum mix spread out over five channels. These could all be sent to one buss output. Same with a group of backup singers on three separate channels. They could also be routed to another individual buss.

Yamaha, on the other hand, counts the regular four busses on their lower end boards, any effect sends, and any monitor sends, and the stereo buss (used for mixdown, or the main FOH output) as a 'buss'.

Shading marketing at best for the unwary and uninitiated.