In the US Ku is divided into 2 main bands and some aux bands. In general the Ku-DBS portion of the band has the satellites separated by 9 degrees. This is what allows the smaller dishes. The satellites are far enough apart that a small dish can see one satellite without picking up the neighboring satellites. The satellites in this band also tend to be more powerful, but that is not a requirement, and some in the Ku-FSS are more powerful than those in the Ku-DBS. Ku-DBS was specifically planned for small dish reception.
Ku-FSS band has satellites spaced 2 degrees apart. This is what requires a larger dish so you can pick out one satellite without receiving the adjacent satellites. If a Ku-FSS satellite did not have neighbors on each side an 18" dish could work with these satellites. These satellites tend to be lower power, but some (like E9 at 140 watts) are more powerful than some ku-DBS (like E1, E2, and E3).
Ka band requires the smallest dish to receive the signal because the frequency is so much higher. But, Ka band dishes are going to have to be larger because of rainfade. Ka is 10x or so more likely to have rainfade, so a larger dish is needed to combat this.
Spot beams can be used by any band (ku-DBS, Ku-FSS, Ka, etc) it is up to the satellite builder to use either one transmit antenna to cover the whole US or use a bunch of antennas, each covering a small portion of the US and allowing them to use the same frequency over and over in different parts of the US. In general spot beam satellites cost a lot more to build and launch, so they are just not as common.