Visual Voicemail versus Live Voicemail

[Wakakanada]

My carrier is pushing a new plan with iPhone 16 but says they won't include Visual Voicemail anymore, just their own Voicemail service Telus - Voicemail 25, which I assume means having to call the carrier service to access the voicemail. Am I correct that IF I get a call when my iPhone is on and not in Low Power Mode, then LIve Voicemail will record and save the message on my iPhone in a similar appearance to a Visual Voicemail [so I can see who called in a list without going into each voicemail], but if I get a call when the iPhone is off or in Low Power Mode, my carrier Voicemail will record the message instead?

Assuming that to be the case, is there some notification that distinguishes between when you have a Live Voicemail message versus a Carrier Voicemail text?

Thanks.