They are two separate lists with two different approval processes, and understanding the difference is useful when you are trying to get on both.
The phone list is managed by the inmate and processed through the facility's phone carrier, whether that is Securus, GTL, IC Solutions, or whoever holds the contract at that facility. The inmate submits numbers they want to be able to call, the carrier runs a basic verification, and approved numbers become active for outgoing calls. The process is relatively straightforward and the inmate has direct control over who gets added.
The visitation list goes through a more rigorous approval process. Prospective visitors submit a formal application to the facility, which includes personal information and consent to a background check. The facility reviews the application and makes an approval decision based on their criteria, which can include criminal history, relationship to the inmate, and other factors. This process takes longer, sometimes several weeks, and the facility has more discretion over who gets approved compared to the phone list.
On your third question about the 20s list, that is a term used in some facilities to refer to the approved contact or correspondence list, which governs who an inmate can exchange written communication with through the facility's messaging systems. In some institutions this is the same as or closely tied to the phone list. In others it is maintained separately. The specific terminology and whether it is combined with another list depends entirely on the facility and the system they use.
The safest approach is to ask the facility directly what lists exist, how each one works, and what you need to do to get on each one.