Abarim Publications' online Biblical Hebrew Dictionary
חבב
The verb חבב (habab) is used only once in the Bible, namely in Deuteronomy 33:3, where it appears to express a term of endearment: "God habab the people." Its sole derivative is the noun חב (hob), which occurs only in Job 31:33: "... by hiding my iniquity in my hob." The verb is commonly translated with "to love" and the noun with "bosom" but there are several other verbs that mean to love (for instance אהב, 'aheb) and the regular and frequently used word for bosom is חיק (heq).
That said, the verb ידד (yadad) also means to love, the noun דד (dad) means nipple, and the noun יד (yad) means hand, so the links are well established. Why Hebrew needs such a rare verb and noun to express the same thing as the verb ידד (yadad) does isn't clear but equivalents in cognate languages suggest that our verb חבב (habab) specifically emphasizes strong emotions or warm or hot feelings. That means that the noun חב (hob) is probably more accurately translated with "embrace" or "clasp".
חבק
Probably not related to the above (the letters ב, b, and ק, q don't normally alternate) and only similar by accident, the verb חבק (habaq) is commonly translated with to embrace. This verb, however, does not emphasize the act of spontaneously and passionately wrapping one's arms around someone else but rather a prolonged standing or laying together with bodies touching, as the result of a search for shelter or safety.
Where the previous verb emphasizes one's emotional motivations, this verb appears to emphasize the physical gathering of one's kin (Genesis 29:13, 48:10) or romantic interest (Song of Solomon 2:6, 8:3, Proverbs 5:20). In Job 24:8 the poor "embrace" a rock for want of shelter, and Lamentations 4:5 likewise speaks of the ruined "embracing" ash pits. Both these instances speak more about prolonged physically huddling together than about passionate embracing.
The noun חבק (hibbuq) literally describes a huddling together. It's used only twice (in the identical Proverbs 6:10 and 24:33) and describes people huddled together in unwarranted idleness (rather than standing with folded arms, as is commonly proposed).