SLIME is much more than just sending code. It's a full-fledged development environment with commands for inspecting variables, viewing threads, stepping, viewing backtraces, etc.
Neat, but not quite the same thing as Slime. Slime also, provides hinting and autocompletion based on the running Lisp image, debugging restarts, namespace resolution and other features.
This seems more general though, and clearly has the biggest feature nailed.
Yes, this is more general and might be useful for other stuff. For an actual slime alternative for vim there is slimv, Superior Lisp Interaction Mode for Vim. http://www.vim.org/scripts/script.php?script_id=2531 I have been toying with Common Lisp using slimv quite successfully.
I use Slimv with Clojure, and love it! You get most of the slime commands, like macroexpand and a REPL in a vim buffer, with doc lookup etc. It even comes packaged with paredit for Vim.
After the most recent bug fixes it has gotten a lot faster, so make sure you get the latest version from https://bitbucket.org/kovisoft/slimv/ - version 0.9.5 on vim.org still has a bug that causes it too slow down.
I use vim-slime every day and am mainly happy with it. It is a little annoying to have to set up screen for it, I wish I knew how to script screen better but the docs are pretty opaque.
You could also use slime in vim with a rube-goldberg-esque combination of eclim (http://http://eclim.org/) and CUSP (http://www.bitfauna.com/projects/cusp/cusp.htm).