Answer: Yes, they do.
Whether or not a trust is a grantor trust, beneficiaries of that trust are deemed to own their pro rata interest of property held by the trust. (Under IRC 1563, there is no attribution to beneficiaries who have less than a 5% interest, determined according to IRS actuarial tables.)
Additionally, if the trust is a grantor trust, then the deemed owner (usually the grantor or settlor) of the trust is deemed to own all of the trust's property.
The rules relating to grantor trusts are detailed and complex. They are the subject of several weeks of a law school course. Although I will quickly summarize them here, these summaries are no substitute for a thorough understanding of the rules. If in doubt, seek advice from a qualified attorney or CPA on the subject.
IRC 673 says a grantor trust exists when the grantor has a reversionary interest of at least 5% of the value of the trust.
IRC 674 says a grantor trust exists when the grantor or a nonadverse party has the power to control who will receive the income or principal from the trust. There are numerous exclusions. Most "living" trusts are grantor trusts because while the grantor is alive he or she retains the right to determine who will receive trust property after he or she dies.
IRC 675 identifies several "poison" administrative powers which will make a trust into a grantor trust.
IRC 676 says a revocable trust is a grantor trust. Thus, all trusts are grantor trusts while the grantor is alive unless the trust is irrevocable.
IRC 677 says a grantor trust exists if income from the trust is payable to (or held for the benefit of) the grantor or the grantor's spouse, or used to pay for their life insurance.
All these rules apply to make the grantor, the person who set up the trust, the deemed owner of trust property. IRC 678 is different. It applies to make a beneficiary the deemed owner of trust property. If the beneficiary has (or has released) the power to vest trust property in him or herself, that beneficiary can be the deemed owner of the trust.
IRC 679 deals with foreign trusts.
Again, this is just a quick summary to let you know the types of issues involved. It is not a substitute at all for a careful review by a qualified professional.
For examples on how the attribution rules apply in trust situations, including grantor trusts, see Chapters 7 and 14 of my book, Who's the Employer.