Thermal Equilibrium (Simple Question)

Question

I'm beginning to revise the basic concepts of statistical mechanics and I came across the definition of thermal equilibrium.

'Two thermodynamic systems are in thermal equilibrium with each other if there is no net flow of thermal energy between them.'

There's also this:

'A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially uniform and temporally constant.'

My question is simple: does the absence of exchange of thermal energy mean that both systems are at the same temperature?

I would answer yes, but I'm still on the fence about this because the commenters of the following post give opposite answers:

Thermal Equilibrium Definition

Answer 1

Yes, you are right- if the two systems are thermally in contact, and we observe no net heat flow between them, then they are at the same temperature.

Answer 2

Well, Everyone saying the same thing, though in a slightly different way.

The two bodies are said to be in thermal equilibrium when the energy content and the temperature of the two bodies cease to change with time.

In the post, Note if there is a flow between the surrounding and $A$, then this means surrounding and $A$ are not in thermal equilibrium. Thus there would be a change in temperature unless surrounding and $A$ come to thermal equilibrium.

The same goes for $A$ and $B$. So the state of thermal equilibrium corresponds to $A$, $B$ and surrounding have the same temperature. That's what has been pointed out by @sam.