"...w
hether this designation makes any significant difference in the trust’s ultimate tax liability?"
When you make distributions in the same tax year as the trust receives income (i.e., there is distributable net income), then that income is passed through to the beneficiaries on the K-1s. The income is then reported on the income tax returns of the beneficiaries and the trust, typically, has no tax liability (unless capital gain is retained within the trust).
In your specific case, it appears as if, (a) you have distributed all trust property to the beneficiaries, (b) the distribution(s) included trust corpus (principal) plus income/gain, (c) you are filing the final return for the trust, and (d) regardless of the foregoing, there was never any requirement in the trust instrument that all income be distributed currently.
Therefore, you would indicate that the trust is a complex trust.
See https://www.irs.gov/instructions/i1041#idm140376226642960
