When only dealing with two layers, "Flatten" and "Merge" should do the same thing: you end up with one layer which you can then "Save As" to produce a final output. Merge can be used to combine more than one layer without including all layers, Flatten will combine all layers in the project. In that case, you may want to Merge so you can do more work with multiple layers, although Merged layers will lose the ability to "fine tune" things on the former layers.
Other things to bear in mind:
1) Once you Flatten or Merge, you can no longer re-visit a particular layer to make adjustments, so don't do it until you are happy with the work you have done!
2) When you Flatten, you are "giving up" your original. Because of this, it is strongly advised that your original (if a jpeg) is preserved as a separate file, so you only do a Save As, rather than a simple Save. If your original is a Raw file, well, it should be preserved.
3) Once you have a "finished" project, if you Flatten it, you are done: you can't preserve the layers for future work. That's fine if that satisfies your workflow, you can put out the project for whatever use and be done with it. However, a lot of people have a workflow in which they want to save a project for future work, and so rather than just flattening and saving a project they'll Save As a tiff or psd with all layers intact, producing a large "project file" but one which can be re-opened with the layers intact so they can be edited/adjusted!
Hey, I'd encourage you to take the time to read up on Elements and on working with layers and such! There are excellent books available as well as great online resources!