What is Matting?
Image matting is the task of separating the foreground from the background in ordinary photos or images, without any special setup like shooting on a green screen.
Most so-called "background removal services" are built on matting.
The goal is to cut out even fine details like hair as naturally as possible. Instead of a simple binary (black-and-white) mask, it produces a mask that also carries semi-transparency, called an alpha matte.
BiRefNet
BiRefNet is a family of foreground extraction models: high-accuracy models specialized for background removal and matte generation.
It's lightweight and performs well, so for matting you can't go wrong with BiRefNet.

There are several variants, but start with general. It handles a wide range of subjects, including people, objects, and animals.
SDMatte
SDMatte is a matting model that draws on what Stable Diffusion knows.

It can cut out the foreground just like BiRefNet, but what sets it apart is that it can handle see-through things like glass bottles, liquids, and thin fabric, at least to some extent.
Like any diffusion-based model, it's computationally expensive, but give it a try when you need to cut out transparent or semi-transparent objects, or extremely fine things like the tips of hair.