Mostly, but not entirely.
Several states including Virginia explicitly recognized slaves that were purely descended from Indians.
It is important to realize that the law often had no bearing on whether a person could be enslaved and there was a huge mismatch between the laws and actual practice. For example, most southern states had laws very early making it illegal to import slaves of any kind and ruling that any slave imported into their state became instantly free. Virginia passed their law of this type in 1792. Nevertheless, this law was never obeyed. Hundreds of thousands of slaves were imported and exported from Virginia after 1792 and none of them that I know of were freed under this law. Another such law, more restrictive, was the Act of 1819 in Virginia, which has the following language:
No persons shall henceforth be slaves within this commonwealth, except
such were so on the seventeenth day of October, in the year one
thousand seven hundred and eighty-five, and the descendants of the
females of them and such persons and their descendants, being slaves,
as since have been, or hereafter may be brought into this state, or
held there in pursuant to law.
Where it was only legal to bring in slaves from other states and the District of Columbia. Thus, for example, it would be illegal to bring an actual African as a slave into Virginia after this law was passed.
As a general rule, after the War of the Revolution the courts only recognized "negroes," meaning Africans, as inherently slaves. Indians could only be slaves if they were the children of slaves and already owned. You could not newly enslave an Indian. If a person imported and enslaved a non-African, that would be illegal, because they were out of limits. The specific language is as follows for Virginia:
- § 3. It shall not be lawful for any person whatsoever, to bring into this state, or to hold therein, any slave or slaves born or
resident out of the limits aforesaid, or any slave or slaves that
shall have been convicted of any offence, and therefor transported by
the laws of this state, or of any state, territory, or district
aforesaid; and, if any person shall bring into this state, contrary to
the provisions of this act, any such slave or slaves, or shall sell,
purchase or hold, in this state, any such slave or slaves, knowing
such slave or slaves to have been brought into this state contrary to
the provisions of this act, every such offender shall forfeit and pay
to the commonwealth, for the use of the Literary fund, for each slave
so brought in, sold, purchased or held, a fine of one thousand
dollars: Provided however, That the penalty aforesaid shall not be
incurred by any person bringing into this state any slave or slaves,
for the purpose only of passing through, or for a short time abiding
therein, if such slave or slaves be not kept within this state for one
whole year, or sold or offered for sale therein.
Notice that there is an exemption for a person "passing through". So, for example, if a foreign diplomat had, say, a Burmese slave and was just traveling through the state, then that would be allowed.
Note that the same laws forbade free negroes or mulattoes from settling in Virginia, as defined by being of one-fourth blood of a negro. Such people could be arrested at will and expelled from the state.