The first command is called Get-WinADTrust. Aside from providing detailed information, it also contains a Recursive switch, which tells the command to try and follow the trusts as much as it can. If we check what, each trust in Get-WinADTrust contains, we're going to get a nice list of properties.
You should notice two properties TrustStatus and QueryStatus. If you're a Domain Admin, what the TrustStatus will do is verify the tunnel using WMI and report if it's working correctly or not. Of course, if you're not Domain Admin, this command won't help as you won't be able to query WMI on Domain Controller. This is where QueryStatus comes in. For each trust, the command queries the Administrator group within that domain. If it can resolve it, the status is OK. If it can't, it's not. This allows you to verify trusts are working or not based on AD Query even as a standard user in your domain. Of course, it's possible the trust is working, but the way it's configured prevents you from querying users/groups on the other end of the trust. That's not all.
Get-WinADTrust has nested properties inside AdditionalInformation property. It includes information like Suffixes used for the trust and their state. This is where I'm using Christ Dent skills to provide the status of a suffix, whether it's enabled, disabled, or in conflict.
You can also see details of the group that was queried while checking trusts. Of course all other stuff such as TGT Delegation status and few others are directly exposed for easy filtering.