Hailing from the scicomp community recently getting into computer-graphics, I have noticed that the scicomp communities talk about mesh-based methods like FDM, FVM, FEM, etc, vs meshfree or meshless methods like SPH (though I like to call them virtual particle methods), but I've never heard them talk about Eulerian approach vs Lagrangian approach, something I hear a lot in computer-graphics communities involved in computational-physics/mechanics, and they never talk about the terms meshfree or meshless, and rarely mention finite-elements.
Would it be correct to say that Eulerian approach is another name for mesh-based simulation, while Lagrangian approach is a synonym for meshfree/meshless?
If not, can anyone clarify, or provide a good reading on this topic? (No need to invoke the boat analogy in which Lagrangian is like sitting in a boat in a river, and Eulerian is like watching the boat from the river bank. I've heard/read/watched that analogy about a dozen times and it has zero comparison to FEM, meshless, meshfree and is therefore useless in answering my question).