REST stands for "representational state transfer", which means it's all about communicating and modifying the state of some resource in a system.
REST gets quite involved, because the theory behind REST gets into leveraging media, hypermedia, and an underlying protocol to manage information on a remote system.
CRUD, on the other hand, is a mnemonic for the common operations you need for data in a database: Create Retrieve Update Delete. But it really doesn't get any deeper than that.
So that's the answer to your question, but I'll mention the common mistake I see when REST and CRUD are discussed together. A lot of developers want to map REST to CRUD directly, because REST over HTTP provides for GET PUT POST and DELETE, while CRUD provides for CREATE RETRIEVE UPDATE DELETE. It's natural to want to map the REST verbs directly to CRUD operations.
However, HTTP uses a "create or update" style, while CRUD separates create and update. That makes it impossible (!) to make a clean, general mapping between the two (!)
GET and DELETE are easy... GET === RETRIEVE, and DELETE === DELETE.
But per the HTTP spec, PUT is actually Create AND Update:
Use PUT to create a brand new object when you know everything about it, including its identifier
Use PUT to update an object (usually with a complete representation of the object)
POST is the "processing" verb, and is considered the "append" verb:
Use POST to append a new object to a collection -- that is, create a new object
POST is also used when none of the other verbs quite fit, as the HTTP spec defines it as the "data processing" verb
If your team is getting hung up on POST, remember that the entire WWW was built on GET and POST ;)
So while there is similarity between REST and CRUD, the mistake I see most teams make is to make an equivalence between the two. A team really needs to be careful when defining a REST API not to get too hung up on the CRUD mnemonic, because REST as a practice really has a lot of additional complexity that doesn't map cleanly to CRUD.