Is there any tax difference between a US citizen and a US lawful permanent resident?

There are some differences in US gift tax if the person's spouse were to give a gift (or leave an inheritance) to the person, although the gift tax would be paid by the giving spouse, not the person him/herself. When the recipient of the gift is a US citizen spouse, the entire gift is not taxable, but when the recipient of the give is a non-citizen spouse (including a permanent resident), there is an annual exclusion of $157,000, and amounts beyond that would count against the giver's lifetime exemption of $11.58 million

For income tax purposes, there is no difference between US citizens, permanent residents ("green-card" holders), and US tax residents (those who are not permanent residents but are residing in the US temporarily, e.g. H-visa status holders, F-visa status holders who have been in the US for five years etc.) They must pay US income tax on their world-wide income, and if they also paid foreign income tax on income generated outside the US, they can get a credit against their US income tax due for the foreign tax paid. For gift taxes, there are different rules for citizens versus non-citizens as user102008's answer notes. I believe that there are similar differences in estate tax rules also.

Answer from Mike Eisler:

My understanding is that considering estate taxes there is a major tax difference.

As a former green card holder this question interested me for a time.

If one spouse in a marriage dies, if the surviving spouse is an alien (including a lawful permanent resident) and the deceased was either:

• a resident of the USA subject to the jurisdiction of the USA (e.g. not a diplomat)
• Non-resident of the USA, and was one of:
  • citizen of the USA
  • a lawful permanent resident (LPR) of the USA
  • a former citizen or LPR deemed have renounced status to avoid income tax

Then the normal spousal inheritance estate tax waiver does not apply.

If the estate exceeds the estate tax exemption, then work around is to set up a qualified domestic trust (QDOT) before the deceased dies and name a trustee who is a USA citizen.

My understanding is that that a revocable living trust can be valid QDOT.

Note that in 2020, the exemption is $11.58 million. However the exemptions fluctuates. In has been as low at $600K.