This question is pretty straight forward. From my knowledge, both forms are written freely without much restriction.
How can I tell the two apart and what are some of the things that make them different?
I assume you seek an empirical answer, but here is a philosophical one. I am giving such an answer because I deem giving the kind of answer which I assume you seek as impossible. Below is my argument for why it is impossible.
Before you evaluate the rest of my argument, please actually looking at what these things look like by following the above links.
To come up with an empirical answer to 'what are some of the things that make a fantasia different from a rhapsody', one can reason by induction: gather exemplars of each concept, and look for commonalities among each set of exemplars, and look for differences between the two sets. One can reason by deduction: formulate a theory of what each concept is by describing a prototype or archetype corresponding to each concept, perhaps using empirical observations from induction, then compare the two theories formulated for differences.
I deny such theory to be useful because composers can always invent new pieces that defy such theory (or 'definition'). For example, imagine historians adjusting their definitions of what a symphony is after Webern composed his Opus 21. Why do theorists define concepts like fantasia or rhapsody (by formulating theories ABOUT actual pieces, using concepts that REFER to empirical observations) even though they know new empirical data (which are man-made instead of occurring naturally) can make such theory obsolete? They do so not necessarily to build theories that are true, but ones that are USEFUL. I now pass a value judgment on your question by saying that the answers to your questions cannot be useful because of my observation of the lack of inducible conceptual differences between actual pieces named as rhapsody and those named as fantasia.
My line of reasoning in the above paragraph may not be so convincing to you because you may not agree with my judgments. I therefore started this answer with a completely different approach: instead of reasoning with you with induction and deduction, I reason with you by analogy, in my questions above as answers. My reference to Webern's Symphony was also meant to be analogous to pieces that have the word rhapsody or the word fantasia in their titles.