How many Borel conjectures are there

Question

The following may be referred to as Borel conjecture:

Every strong measure zero set of reals is countable.

On the other hand Wikipedia refers to the following as the Borel conjecture:

Let $M$ and $N$ be closed and aspherical topological manifolds, and let $f:M\to N$ be a homotopy equivalence. The Borel conjecture states that the map $f$ is homotopic to a homeomorphism.

The two seem to be unrelated. Is the naming confusing coincidence? Or are they related? Moreover are they really still conjectures or were they subsequently solved? The article I link to does not mention the status of the "conjecture(s)".

Answer 1

These Borels are different people.

The first one is Émile Borel, whereas the second one is Armand Borel. From the latter's Wikipedia page,

He used to answer the question of whether he was related to Émile Borel alternately by saying he was a nephew, and no relation.