Are Hakko tips cross-compatible?
No, Hakko tips that are different series are, well, different.  Now, officially, Hakko states that a given iron can ONLY use the series of tips designed for it. 
 In your case, that's the T18 series.  Unofficially, the older 900M tips are known to work with any iron that uses T18 tips.  Though they won't last quite as long, as I believe the 900M tips are rated for 60W, while the T18 tips are rated for 65W.  

Also, unofficially, the T12 and T15 tips are compatible, and I am not quite sure what the deal is with those.  T15 tips seem to just be T12 tips but for the North American market.  Other markets have T12 tips.  The output voltage is the same, and there is a large amount of anecdotal evidence that seems to suggest there is no meaningful difference between them and you can use either T15 or T12 tips with the correct iron.  Note that the correct iron is NOT an FX-888/D. 

Just to drive this point home, this is nothing to do with some inner or outer diameter.  The tips are not even remotely functionally similar.

These are T12/T15 tips: 



They contain their own ceramic heating element, and slide into a female receptacle in the soldering iron handle.  They're designed to be used with a completely different style of iron than the FX-888D.  They are about as compatible as oil with water.  Unfortunately, if you want to use some of those more interesting SMD tips, you'll need to buy one of the irons that uses them (or a cheaper knock off, which can use those tips as well).