The OP asked:
Galatians 3:10 says that "as many as are of the works of the law [as opposed to those who live by faith] are under the curse." Is this different from being accursed [as described in 1:8]?
This question about a possible difference between the sort of curse in Gal 1:8,9 and Gal 3:10 seems to have not been addressed so far. For reference (NA28 | ESV):
Galatians 1:9 (v. 8 similarly)
εἴ τις ὑμᾶς εὐαγγελίζεται παρ᾿ ὃ παρελάβετε, ἀνάθεμα ἔστω.
If anyone is preaching to you a gospel contrary to the one you received, let him be accursed.
Ὅσοι γὰρ ἐξ ἔργων νόμου εἰσίν, ὑπὸ κατάραν εἰσίν· γέγραπται γὰρ ὅτι ἐπικατάρατος πᾶς ὃς οὐκ ἐμμένει πᾶσιν τοῖς γεγραμμένοις....
For all who rely on works of the law are under a curse; for it is written, Cursed be everyone who does not abide by all things written...
There are indeed two different expressions here translated “[ac]cursed”.
ὑπὸ κατάραν....ἐπικατάρατος (3:10)
As noted in another answer (which appears to mistakenly consider it an example of ἀνάθεμα), this is a reference to Deuteronomy 27:26 (Rahlfs | BHS):
Επικατάρατος πᾶς ἄνθρωπος, ὃς οὐκ ἐμμενεῖ ἐν πᾶσιν τοῖς λόγοις τοῦ νόμου τούτου τοῦ ποιῆσαι αὐτούς·...
...אָר֗וּר אֲשֶׁ֧ר לֹא־יָקִ֛ים אֶת־דִּבְרֵ֥י הַתּוֹרָֽה־הַזֹּ֖את לַעֲשׂ֣וֹת אוֹתָ֑ם
Here, as with nearly all 40 times the word is used in the LXX, it translates the Hebrew ʾārûr.1 The passive participle ʾārûr is used primarily in the “ʾārûr formula": "ʾārûr is X" or "ʾārûr is the one who...”. This forms the semantic opposite of the blessing formula using bārûk. Jenni-Westerman explain the meaning:
The ʾārûr formula has a double function. First, it designates a particular person...as ʾārûr, i.e., it covers the person with disaster through the medium of the effectual word.... Second....it creates a curse zone, i.e., a potential disaster sphere, into which the one who commits the deed named in the formula enters... 2,3
In its New Testament usage, the meaning of επικατάρατοςis generally extended from the “effectual word” of the one speaking as a statement that the individual is already condemned by God or are under threat of condemnation.4
The nature of the coherence between the first and second statements of the curse in 3:10 is a matter of much debate and is beyond the scope of this answer. The basic options are that the first statement is meant to indicate that those under the law are cursed because (1) no one can keep the law perfectly; or (2) one cannot, in any case, be justified by works of the law. F.F. Bruce discusses this in considerable detail and finally favors the latter.5
Regardless of how one synthesizes 3:10, the meaning of "ἐπικατάρατος" is closely tied up with 3:13 where Paul cites Deut 21:23 (LXX: κεκατηραμένος; Paul changes this to ἐπικατάρατος) to support his contention that Christ redeemed believers from this curse, γενόμενος ὑπὲρ ἡμῶν κατάρα (by becoming a curse for us). This "exchange curse" is central to Paul's understanding of the notion of ἐπικατάρατος.
ἀνάθεμα (Gal. 1:8-9)
This term been addressed in prior answers. For completeness, I note that, like ἐπικατάρατος, ἀνάθεμα6 has a consistent LXX correspondent: the Hebrew ḥērem. This is a technical expression describing something that has been taken out of common usage and dedicated to the LORD for destruction, a "ban gift". This can at times be applied to people, with a complicated variety of specific implications. People disagree on the extent to which Paul's usage of ἀνάθεμα carries the idea of ḥērem. Regardless,
the controlling thought [in Paul's use of ἀνάθεμα] is that of delivering up to the judicial wrath of God one who ought to be ἀνάθεμα because of his sin. 7
Galatians 1:8 shares with most of the usages in the Pauline corpus a volitional mood (let him be accursed). Paul is following a curse formula known in ancient Greek literature, both in the political and personal realms, an "official conditional curse", expressed using the imperative or optative mood.8 The conditional nature means that it will be activated only if a wrong is committed.
[C]onditional curses act as a deterrent against behavior perceived as a threat to society or the political order.9
The basic gist is that of a prohibition.
The uses of “accursed” in Galatians 1:8,9 and 3:10, then, share the idea of God’s condemnation on the one so labeled, but they have distinct backgrounds. Galatians 1:8,9 echo an ancient Greek formula used as a deterrent to aberrant behavior. Galatians 3:10 invokes the ʾārûr formula of the Hebrew Bible, announcing divinely sourced disaster.10
1. In turn, the 41 instances of ʾārûr are translated in every instance by επικατάρατος or a related form.
2. For an elaborate example of what the life of one who is ʾārûr looks like (courtesy of J-W, below), see Deut 28:15–68.
3. C. A. Keller, “ארר,” Jenni & Westermann (eds), Theological Lexicon of the Old Testament [TLOT], (Hendrickson Publishers, 1990).
4. “ἐπικατάρατος,” Johannes P. Louw and Eugene Albert Nida, Greek-English Lexicon of the New Testament: Based on Semantic Domains (New York: United Bible Societies, 1996).
5. F. F. Bruce, The Epistle to the Galatians: a Commentary on the Greek Text (NIGTC; Grand Rapids: Eerdmans, 1982).
6. In ancient Greek and occasionally in the LXX, alternatively spelled ἀνάθημα.
7. Behm, “ἀνατίθημι,” *Theological Dictionary of the New Tesatment, Kittel & Friedrich (eds), 1:353–56.
8. Although it may not be obvious in English, this contrasts with the Greek of Gal 3:10 and the usual structure of the ʾārûr formula, which is that of a noun clause ("cursed [is] the one..."), not (at least explicitly) a volitional construction, and more often construed as a pronouncement.
9. "Oaths, Curses,” Kyriaki Konstantinidou. From Encyclopedia of Ancient Greek Language and Linguistics, Georgios K. Giannakis (ed), Brill online, accessed 09/26/2015.
10. Another way to think about the difference between ἀνάθεμα and ἐπικατάρατος, at least insofar as the terms follow their Hebrew counterparts, is to consider their antonyms. The opposite of ἐπικατάρατος/ʾārûr is blessed (barûk=εὐλογητὸς). On the other hand, ἀνάθεμα/ḥērem (within the realm of sacred) forms a contrast with holy (qōdeš=ἅγιος) in one plane and profane (ḥôl=βέβηλος) in another.