No, all sin is not willful. There's a difference as the Lord has said. Willful sin is unacceptable to the Lord, but unintentional sin can be forgiven.
Numbers 15
[27] And if any soul sin through ignorance, then he shall bring a she goat of the first year for a sin offering.
[28] And the priest shall make an atonement for the soul that sinneth ignorantly, when he sinneth by ignorance before the Lord, to make an atonement for him; and it shall be forgiven him.
[29] Ye shall have one law for him that sinneth through ignorance, both for him that is born among the children of Israel, and for the stranger that sojourneth among them.
[30] But the soul that doeth ought presumptuously, whether he be born in the land, or a stranger, the same reproacheth the Lord; and that soul shall be cut off from among his people.
[31] Because he hath despised the word of the Lord, and hath broken his commandment, that soul shall utterly be cut off; his iniquity shall be upon him.