- Was I out of status? or violated any F1 rules?
Yes, you were out of status after your grace period was over, 60 days after completing your OPT.
- Have I accrued 150 days of unlawful presence
No, you almost certainly did not accrue any days of "unlawful presence". "Unlawful presence" only starts accruing under one of 3 situations:
- You stay past the date on your I-94.
- You apply for a benefit to USCIS, and are denied together with a determination that you are out of status.
- You are placed in removal proceedings in immigration court, and are ruled out of status by the immigration judge.
As an F1 student, you were almost certainly admitted for "D/S" on your I-94, instead of a date. People admitted for "D/S" cannot meet the first condition above, so they do not accrue unlawful presence unless either of the latter two conditions happen (i.e. they must have applied for a benefit to USCIS, or were placed into removal proceedings). I am assuming that neither of these things happened.
See USCIS Adjudicator's Field Manual chapter 40.9.2(b)(1)(E)(ii) (on page 76 of this PDF):
(ii) Nonimmigrants Admitted for Duration of Status (D/S). If USCIS
finds a nonimmigrant status violation while adjudicating a request for
an immigration benefit, unlawful presence will begin to accrue on the
day after the request is denied. If an immigration judge makes a
determination of nonimmigrant status violation in exclusion,
deportation, or removal proceedings, unlawful presence begins to
accrue the day after the immigration judge's order. It must be
emphasized that the accrual of unlawful presence neither begins on the
date that a status violation occurs, nor on the day on which removal
proceedings are initiated.
And 9 FAM 302.11-3(B)(1).b(2):
b. (U) DHS has interpreted "period of stay authorized by the Secretary
of Homeland Security," as used in this context, to include individuals
who:
(2) (U) were inspected and admitted for "duration of status" (DOS),
any period of presence in the United States, unless DHS, an IJ, or the
BIA makes a formal finding of a status violation, in which case
unlawful presence will only being to accrue the day after the formal
finding is made;
which is further reinforced in 9 FAM 302.11-3(B)(1).d:
d. (U) Unlawful presence will not accrue for persons who have been
admitted for duration of status (DOS) (as is usually the case with
individuals in A, G, F, J, and I visa status), unless DHS, IJ, or the
BIA finds a status violation in the context of a request for an
immigration benefit or during removal proceedings. This finding of
status violation by the DHS, an IJ, or the BIA will cause a period of
"unlawful presence" to begin. In DOS cases where DHS or an IJ or the
BIA makes a formal status violation finding, the individual begins
accruing unlawful presence on the day after the finding (i.e., the
date the finding was published /communicated). For example, if an
applicant presents a letter from DHS dated December 1, 2008, that says
the applicant was out of status starting on May 28, 2001, the
applicant began to accrue unlawful presence as of December 2, 2008,
not May 28, 2001.
(Note that USCIS put out a memo in 2018 that sought to make people in F and J status accrue unlawful presence when out of status starting in 2018, but this was blocked by the courts, and DHS accepted the court's decision. See this page for a summary of the litigation history. A preliminary injunction was granted on 5/3/2019, and a permanent injunction on 2/6/2020. On 7/31/2020 DHS asked to dismiss its own appeal, and the court granted it on 8/3/2020. As you can see from the above quotes, the current USCIS Adjudicator's Field Manual does not include the changes from the memo.)
and how it differs from overstay?
"Overstay" is not a well-defined term in immigration law.
Your advice will also be helpful for me in answering "Have you ever been unlawfully present or overstayed or violated any terms of a U.S. visa" when completing DS160 for a new F1.
You will have to answer Yes since you violated the terms of F1, even though you did not accrue unlawful presence.