Was owning slaves in the US limited solely to black people? Could somebody own white slaves?

After a brief search, I was fascinated to learn there was not a longer thread on this available. I have looked at the /u/sowser response and agree that it might be of interest to you. I would also recommend this post from /u/JAT621 about the relationship between slave labor and working white wages in the Antebellum south because I think it's important.

Picking up from /u/gnikivar2's response below I'd like to comment on the relationship between slavery, indigenous peoples, whites, and Africans. The idea of chattel slavery in the colonial south is nearly as old as the colonies, with the first African slaves brought to Jamestown only a decade after the colony was founded. It is accurate that the English, French, and Spanish experimented with indigenous slavery prior to the widespread introduction of African chattel. In North America, however, practices of indigenous slavery were different that African chattel slavery that was introduced on a large scale at the end of the seventeenth century. Brett Rushforth's Bonds of Alliance does a wonderful job in demonstrating that indigenous slavery existed prior to European arrival in the North America but operated much differently. Rather than serve as possessions, indigenous slaves were often incorporated into the community during "mourning wars" intended to replace community members who had been lost during battle. Other "slaves" were traded between peoples as offerings of peace. The French fur trappers in the Pays d'en Haut practiced this form of indigenous slavery and some English western frontier settlers in the seventeenth century also followed these practices.

The question about the relationship between indentured servitude and slavery is indeed an important one. I would recommend Wareing's important new book Indentured Migration and the Servant Trade from London to America, 1618-1718, which demonstrates how pivotal the trade in indentured servitude was for both populating the American colonies and serving as an outlet for landless poor in urban England. Wareing also demonstrates that coercion and deceit were foundational to supplying the southern colonies with indentured servants to preform labor. Many servants were young and brought across the Atlantic to supply labor. While there were different forms of servitude with some being more favorable than others, few servants were able to secure lucrative contracts and most were subject to forms of exploitation.

This of course, however, IS NOT chattel slavery because servants were entitled to rights that slaves were denied. It is important to note that the earliest African slaves imported to places like Virginia and Carolina, were not held in lifelong bondage. Rather, many slaves were granted manumission later in life and there was a sizeable free African population in the English colonies. Exactly when this period ended is hotly contested in the historiography. Edmund Morgan's American Slavery American Freedom argues that growing collaboration between a large indentured servant and enslaved African population culminated in the mixed race Bacon's Rebellion, which demonstrated to the ruling hierarchy of Virginia that the two classes needed to be separated. The result was lifelong bondage based on race for African slaves. In his White Over Black, Winthrop Jordan contests that the English were predisposed to racial thought long before the late seventeenth century. Regardless, European demand for plantation products like sugar, tobacco, and eventually cotton in the eighteenth century cemented the need for labor in the American south, throughout the Caribbean, and into Latin and South America. Despite experimentation with other forms of labor, enslaved African chattel became the most economical and proven method of agricultural production. The result in the English colonies was a deeply entrenched socio-economic system of slavery that relied on constructed radicalized difference.

TL;DR: Chattel slavery developed with the increasing importation of African slaves. While there were other forms of bondage that "enslaved" white and indigenous peoples alike, only Africans were ever held as chattel on wide scale.