Historically, "homesteading" refers to both a legal principle of claiming "unclaimed" natural resources which forms a strong foundation in many anarcho-capitalist philosophies, and a self-sufficient lifestyle on a "homestead", a dwelling which may have isolation from those around it but retains it's origin in the original legal principle - or is enabled by a government for physical expansion. Both of these uses of the term have a strong background in space colonization and are now still relevant to certain activities by the Inner System.
Luna and Venus do not have good terrain for classical homesteading either way, and required too much structure and technical assistance to settle. Mars, on the other hand, has much more land availability - and so in the early colonization period it was not uncommon for governments and early corporations to offer "homestead" plots for cheap on scales similar to classical Homestead Acts, often with caveats about terraforming or legal taxation. These systems enabled the diaspora of certain small settlements on Mars pre-Fall, and lead to the small croppings of homesteads, smallholds, compounds, etc which can still be seen in some regions today - though due to the rough environment of Mars, nomadic life was preferred.
After the Fall, the legal issues of "de-nationalization" for many colonies, the rise of the Tharsis League and the Planetary Consortium and their cooperation via the TTO on terraforming issues threw the legality of some prior homesteading for a loop. Relocations due to the TQZ or terraforming was not uncommon, and corporations often got first choice on acquiring new land. But the influence of the Martian city states can only go so far, and the Tharsis League wished to lend structure to the outback in some way - leading to the revival of some legal homesteading acts. This was done to appease rural martians and nationalists, but also had the approval of the Planetary Consortium. For hypercapitalists, the homesteads promote a middle class of consumers who can be marketed to for luxury goods or are otherwise engaged in the system - for the Barsoomians the hope is to gain control of land seperate from the hypercorps and promote self-sufficient living. Ultimately, neither side got their exact desire out of the resulting legal framework - but should political shifts occur strongly one way or the other the League's rules could help promote influence for either side.
The basic way this functions is handled in a Homesteading contract. Similar to an indentureship, but with the focus on land instead of a morph and with different labor expectations. The homesteader buys the land from the Tharsis League (or occasionally an interested hypercorp) for a much reduced fee or in payment over a period of years, usually 5-10. In exchange, they must live on and work on the property for the duration of the contract - after which point the provisions are removed, and the land is fully legally owned by the homesteader who can do with it what they will. Typically "working the land" often has provisions to aid in terraforming operations - which can sometimes breed tension between homesteaders and Nomads. Tharsis contracts are generally fairly plain, other than the requirements to follow TTO guidelines - but also often lack support, being fully self-sufficient farms. Corporate contracts tend to involve more legal complexities and components aimed to bring profit to the corporations, such as a famous instance where Fa Jing homesteaded a large plot of land, but retained the legal right to seize back any land where the Homesteader discovered mineral deposits - basically arranging a scheme where people paid to survey land for minerals.
Homesteading is not as popular on Mars despite it's origins as it is with the Pathfinder corporation on Exoplanets. Homestead contracts are intended to bring in those "middle class" colonists who are already instanced and may not require a new morph but can still provide valuable skills and labor to colonies in non-specialist ways. While these contracts involve more varied terrain and support, many, such as in the Outer System, see them as slightly more predatory - the unspoken constraint being that all supplies must come and go through the Pandora Gates controlled by Pathfinder.
As a legal principle, homesteading is also a huge aspect in asteroid families and regions, like the Main Belt. It's one thing to claim to own an asteroid from several AU away - it is entirely another thing to actually settle on it and begin to work it. This sort of attitude drove the success of many strains of Extropian thinking in early asteroid colonization and mining. While corporations and governments would lay claim to asteroids, very rarely did the greater transhuman community uphold such claims unless the claimant could show they were willing and capable to physically access and produce from the body - cutting down on entities attempting to extort others by holding and selling legal rights to an object they would never practically exert control over. As hypercorps grew in power and influence in the time immediately before the Fall, however, several militant expulsions of "squatters" occurred, which may drive why self-defense is a strong meme in many brinker and Extropian clades.
Even now, there is a strong aspect of the homesteading principle to Belters. If you can land on a rock and live and work it, it's yours. You get first say on who else can work and live on the rock, and have a right to protect yourself from aggression against it. Due to desire to work with independant Belters and Extropians, many less militant hypercorps have taken the hint and prefer to buy out small communities who settle on asteroids they desire. Homesteading is not as popular in the Outer System excepting Extropian circles. The Jovians have no excess land to homestead, and groups such as the Commonwealth do not hold much with the principle for their socialist or communist ideals. That said, there is a similar provision for those who are reputable to live on their own in the Titanian wilderness, both in nomadic and structured form - just that the unspoken contract is that excess resources will be shared with the wider community.