Since the various checkuser-verdict templates have a wide range of possible interpretations, this is a description of what I am trying to communicate by using each of them. I hesitated to make this, both from a BEANS perspective and because two different cases can have the same outcome for wildly different reasons, but I'm going to try to put each one into words without losing the level of generality that they provide.

It's important to note that these are always used in the context of the entire case, including not only the data provided by the Checkuser on the users involved, but also my general impressions based on the ISP and IP ranges involved. For example, if user A and user B both share an IP address and user agent, they could be  Confirmed (if no one else has used that IP address), or  Likely (if there are a few other users on that IP address), or I could even downgrade it to  Possible (if there are tons of unrelated users on the same IP address).

Template Description What to do with it?
 Confirmed I am confident that these accounts are operated by the same person. The accounts are an exact or near-exact match on IP address, on a small IP range (like an IPv4 /24 or an IPv6 /64), or on multiple larger ranges. If there are any other users on the same IP address or range, the technical similarities between the {{confirmed}} accounts (such as the devices and browsers they use, or the times that they change IP addresses) clearly set them apart from any other users on that range. The accounts should have already been checkuser-blocked.
 Technically indistinguishable There is strong technical evidence connecting these accounts, but more behavioral investigation may be necessary. I use this when I want to place an emphasis on the "technically" part, usually when the Checkuser turns up additional accounts that were not included in the initial report. The accounts are technically similar, but I have looked enough at the behavioral evidence to decide whether to block. I should include an explanation when I use this. The accounts need additional behavioral investigation, after which any admin can block them if necessary. If you block them, please link to the SPI case page. Do not use the {{checkuserblock-account}} template unless you are a checkuser, tag their userpage using {{sock|master's username|blocked}}.
 Likely I believe that these accounts are operated by the same person, but the technical evidence is not strong enough to say "confirmed". They may be using the same ISP, but never have used the same IP addresses, or there may be too many other users on the same IP ranges to clearly set the sockpuppets apart from other accounts. This is still a positive result - the {{likely}} accounts have some technical data in common. If they haven't already been blocked, evaluate the behavioral evidence and block if you find it at least reasonably convincing. The {{likely}} result is a point in favor of blocking, but is not enough to block on its own.
 Possilikely (a mix between possible and likely) I try not to use this anymore. If I do, it's essentially a weak "likely".
 Possible The technical evidence neither confirms nor rejects the theory that these are sockpuppets. Must be decided behaviorally. Evaluate the behavioral evidence and block if you find it convincing. The {{possible}} result is not evidence in either direction.
 Unlikely The accounts do not appear to be sockpuppets. The accounts are using different ISPs, different devices, or are in different locations. While the possibility cannot be completely discounted, the evidence is pointing towards the accounts being separate users. As below, this is more than just an absence of evidence, but (weak) evidence that the accounts are not being operated by the same person. Evaluate the behavioral evidence and block if you find it convincing. The {{unlikely}} result is a point against blocking, but it can be overcome if the evidence in favor is sufficiently convincing.
Red X Unrelated I am confident that the accounts are operated by different people. This is a stronger form of "unlikely". It generally means that the accounts are operating from different ISPs, in different locations, and I trust the geolocation data / ISP identification enough to rule out the possibility that they are evading checkuser. Note that this is not just an absence of evidence, but rather positive evidence that there is no connection. Evaluate the behavioral evidence and block if you find it convincing. The {{unrelated}} result is a (strong) point against blocking, but it can be overcome if the evidence in favor is sufficiently convincing.
 Inconclusive It's fairly rare that I'll use this. The most common reason is that at least account is using a proxy or VPN, but even then, I'll usually use {{possible}}.
 Stale There is no data available because the account has not edited within the last 90 days.