An accelerator generally takes a small percentage of equity in externally driven ideas in exchange for small amounts of capital and coaching. There is usually a program that an entrepreneur can sign up for ranging from 3 to 6 months in duration but most are in the range of 3 to 4 months. An incubator generally takes a longer-term view and may prepare you for an accelerator. It is primarily trying to help the entrepreneur vet, validate and refine their solution. There are even pre-accelerators that prepare you for an accelerator and last between 4 and 8 weeks long. A great directory from the State of Texas on Texas incubators, accelerators, and resources can be found here. It's a bit dated (2017) but still useful.

Co-working is a shared working environment, many times an office setting, with different small businesses or startups working independently side by side. Unlike in a typical office environment, space is filled with companies that don't belong to the same organization. Co-working can be a cost-effective way to have an office without the burden of owning a building.