At high levels (meaning you've built up some nice Forth words), I disagree. The main difference is that most Lisps and Schemes have a GC, so you're not in charge of allocating/freeing memory like you would in Forth. That doesn't stop Forth words from implicitly referring to a variable that actually contains memory allocation addresses and hiding the actual underlying details of the allocation.

I think Forth certainly starts you out at a level of abstraction only somewhat more rich than an assembler while a Lisp runtime certainly abstracts more away from you, but once a Forth has been built-up, they become similar. Gforth gets a lot of flack in the Forth community for not being minimal, but it's a good example of a feature-rich Forth with support for things like exceptions, filesystems, sockets, and more. The Forth community itself is split into broadly two camps. The minimalist camp, (where Chuck Moore likes to live) which believes in bringing up custom Forths for custom platforms, creates small Forths that try to limit abstraction. The more featureful ANS Forth community tries to focus on a more batteries-included experience and these have more in common with most Common Lisp and Scheme runtimes.