Thomas Markov’s answer covers the ability’s phrasing and the Border Ethereal topic sufficiently.
I want to add onto that, however; Xanathar’s Guide to Everything features an eldritch invocation for warlocks called “Ghostly Gaze” (p. 56/57):
Prerequisite: 7th level
As an action, you gain the ability to see through solid objects to a range of 30 feet. Within that range, you have darkvision if you don’t already have it. This special sight
lasts for 1 minute or until your concentration ends (as if you were concentrating on a spell). During that time, you perceive objects as ghostly, transparent images. Once you use this invocation, you can’t use it again until you finish a short or long rest.
This invocation elaborately describes gaining the ability to see through solid objects and how you perceive them (as it would be very inconvenient if you couldn’t see solid objects at all while using the invocation).
If Truesight were intended to grant the same benefit, we would expect it to have a similarly accurate phrasing. Remember: in 5e, rules only do what they say.
As a sight note, if you want to see around corners or behind solid objects, Blindsight may be what you’re looking for:
A creature with blindsight can perceive its surroundings without relying on sight, within a specific radius. Creatures without eyes, such as oozes, and creatures with echolocation or heightened senses, such as bats and true dragons, have this sense.
It’s not explicitly stated that this allows looking around corners, but it’s how I interpret it.