"IFF" (if and only if) vs. "TFAE" (the following are equivalent) If $P$ and $Q$ are statements,

$P \iff Q$

and

The following are equivalent:
$(\text{i}) \ P$
$(\text{ii}) \ Q$

Is there a difference between the two? I ask because formulations of certain theorems (such as Heine-Borel) use the latter, while others use the former. Is it simply out of convention or "etiquette" that one formulation is preferred? Or is there something deeper? Thanks!

"TFAE" is appropriate when one is listing optional replacements for some theory.  For example, you could list dozen replacements for the statements, such as replacements for the fifth postulate in euclidean geometry.
"IFF" is one of the implications of "TFAE", although it as $P \rightarrow Q \rightarrow R \rightarrow P $, which equates to an iff relation.  
