Clarifying on how if p,q is logically equivalent to p only if q Here is what my book says about the different ways implications are worded 

I am struggling with how "if p, then q" is logically equivalent to "p only if q"
The example I came up with 
With "if p, then q" - If Russell plays in the NFL, he plays football.
With "p only if q" - Russell plays in the NFL only if he plays football.
Say Russell plays in the NFL, plays football and plays soccer. 
With regards to that statement, my thought would be that "If Russell plays in the NFL, he plays football" implication would evaluate to true because Russell plays in the NFL and he plays football. However, with regards to "Russell plays in the NFL only if he plays football", wouldn't this evaluate to false because it says that the only way for Russell to play in the NFL is if he plays football. That means that playing football and soccer would not be a path for Russell to play in the NFL because it is not the  defined only way, only playing football. 
Can someone clarify this?
 A: Your example is a little difficult to work with because there is only one "Russell".
Let $p$ = "$x$ plays in the band" and $q$ = "$x$ is interested in music".
The statement $p \to q$ asserts that:


*

*if someone plays in the band, they are interested in music

*if someone plays in the band then they are interested in music

*if someone plays in the band implies they are interested in music

*someone plays in the band, only if they are interested in music


The last one is awkwardly phrased and probably easier to understand phrased the other way around:


*

*Only if someone is interested in music might they play in the band. 

*Only those interested in music play in the band
Essentially the statement, and each of these attempts to phrase it in English, states that the truth extent of $p$ is entirely contained within the truth extent of $q$.
A: "If $p$ then $q$" means

"Whenever $p$ is true, $q$ is true as well" which means

"It is impossible for $p$ to hold true while $q$ does not hold" which means

"In order for $p$ to hold true, $q$ must hold true as well" which means

"$p$ holds true only if $q$ holds true", or, for short

"$p$ only if $q$"
A: "If $p$ then $q$" is definitely not the same as "$p$ only if $q$". The latter statement has the phrase "if $q$" built into it, which could be seen as an indication that it is not the same as the former. In fact, "$p$ only if $q$" is logically equivalent to "$q$ implies $p$". I'm guessing that the textbook was misread? But if you textbook is really asserting that "$p$ then $q$" $\iff$ "$p$ only if $q$" then that textbook is wrong. 
A: "If $p$ then $q$" certainly seems to be logically equivalent to "$p$ only if $q$. See here and here, for example.
