At least in the context of PKCS#5 (which is commonly seen through the encryption of PEM files), DES-EDE3-CBC is Triple DES with three keys, used in CBC mode, with unspecified padding.
Yes, “EDE” means encrypt-decrypt-encrypt for encryption (and decrypt-encrypt-decrypt for decryption). It's implicit in “triple DES” anyway: choosing which direction is encryption and which one is decryption is arbitrary, but the de facto standard choice for triple DES is that 3DES encryption does more 1DES encryption than decryption and 3DES decryption does more 1DES decryption than encryption.
NIST SP 800-67 calls Triple-DES “TDEA”. “Triple-DES”, “3DES”, “DES3”, “TDEA”, “3DES-EDE”, “DES3-EDE”, “DES-EDE3” are synonyms, with one possible nuance, which is the number of different keys.
Triple-DES uses three keys: encrypt with $K_1$, decrypt with $K_2$, encrypt with $K_3$ (for the encryption direction). Obviously if $K_1 = K_2$ then the first two steps cancel out, and if $K_2 = K_3$ the last two steps cancel out, so $K_2$ must be distinct from both $K_1$ and $K_3$. It is possible to choose $K_1 = K_3$, however. This is called “two-key Triple-DES” (and variant names), while Triple-DES with $K_1 \ne K_3$ is “three-key Triple-DES”. More precisely, “three-key Triple-DES” means that $K_1$ and $K_3$ (and of course $K_2$) are generated independently (so there's a $2^{-56}$ chance of them being equal, but the probability of the easier attack is commensurably small with the amount by which it's easier, so that's no worse than “there's a $2^{-56}$ chance that the key is one specific value for which the attacker has precomputed tables”).
Due to the possibility of meet-in-the-middle attacks, three-key Triple-DES is almost as easy to break as two-key Triple-DES. (And the same attack makes double-DES almost as easy to break as single-DES, which is why double-DES isn't used.) Nonetheless, two-key Triple-DES has been deprecated for longer than three-key Triple-DES.
“Triple-DES” or “3DES-EDE” is ambiguous in whether using only two keys (i.e. $K_3 = K_1$) is permitted. Spelling it “DES-EDE3” is likely an indication that three distinct keys must be used. However, you need to check the specification of each protocol, since the subtle spelling distinctions are not always universally recognized. For example, PKCS#5 specifies that it is “three-key triple-DES”; writing out “three-key” does mean that the keys must be independent.