Prosperous Etymology

I was having a conversation about the economy last week, and my friend was talking about how to thrive in a recession.  And I recommended thrift.  Which made me think.  Thrift and Thrive have very similar spellings.  Are they related?

Thrift - c.1300, "fact or condition of thriving," also "prosperity, savings," from M.E. thriven "to thrive" (see thrive), possibly infl. by O.N.þrift, variant of þrif "prosperity," from þrifask "to thrive." Sense of "habit of saving, economy" first recorded 1550s

Spendthrift - c.1600, from spend + thrift in sense of "savings, profits, wealth." Replaced earlier scattergood (1570s) and spend-all (1550s).

Prodigal - mid-15c., back formation from prodigiality (mid-14c.), from O.Fr. prodigalite (13c.), from L.L. prodigalitatem (nom. prodigalitas) "wastefulness," from L. prodigus "wasteful," from prodigere "drive away, waste," from pro- "forth" + agere "to drive" (see act). First ref. is to prodigial son, from Vulgate L. filius prodigus (Luke xv.11-32).

(see also the American Heritage Definition #2 of Prodigal: Giving or given in abundance; lavish or profuse)

Profuse - early 15c., from L. profusus "spread out, lavish, extravagant," lit. "poured forth," prop. pp. of profundere "pour forth," from pro-"forth" + fundere "to pour" (see found (2)).

Wastrel - "spendthrift, idler," 1847, from waste (v.) with pejorative suffix (cf. mongrel, scoundrel, doggerel).

Thrive - c.1200, from O.N. þrifask "to thrive," originally "grasp to oneself," probably from O.N. þrifa "to clutch, grasp, grip" (cf. Swed.trifvas, Dan. trives "to thrive, flourish"), of unknown origin.

Prosper - mid-15c., from O.Fr. prosperer (14c.), from L. prosperare "cause to succeed, render happy," from prosperus "favorable, fortunate, prosperous," perhaps lit. "agreeable to one's wishes," from Old L. pro spere "according to expectation," from pro "for" + abl. of spes "hope," from PIE base *spei- "to flourish, succeed."

Flourish - c.1300, "to blossom, grow," from O.Fr. floriss-, stem of florir, from L. florere "to bloom, blossom, flower," from flos "a flower" (seeflora). Metaphoric sense of "thrive" is mid-14c. Meaning "to brandish (a weapon)" first attested late 14c. Related: Flourished;flourishing. The noun meaning "literary or rhetorical embellishment" is from c.1600.

To God be all glory.