Agreeing with @otus but adding more background and context than I think belongs in comments:
This is an OpenSSL question though you don't say so; all other SSL/TLS software I've looked at uses the RFC spellings DHE ECDHE DH_anon ECDH_anon, but OpenSSL was written yonks ago with EDH in some places (mostly the ones dating before ECC was introduced and there was no ECDH to confuse with EDH) and ADH and AECDH in all. You may not have observed the latter two because all unauthenticated suites are disabled by default and very rarely used. So far the devs have been reluctant to "fix" spelling because that could break config files, scripts, calling applications, etc. Especially since OpenSSL cipherstrings are so arcane there seems to be a whole stratum of websites confidently ordaining "the single good way to configure ciphers in openssl or $thing_using_openssl", nearly all of them different and many of them long out of date or completely wrong.
If you look at the cipher details with
openssl ciphers -v [$cipherstring] you will see which key-exchange and authentication methods (and also data cipher and MAC) are used for a given ciphersuite. In recent versions if you use
-V (cap vee) it also shows the code value sent on the wire, which you can match to the RFCs to be 100% certain it is really the same thing.
A few months ago there was discussion on the maillist about accepting the standard spellings while still preferring the OpenSSL ones. See
http://rt.openssl.org/Ticket/Display.html?id=3203 (guest/guest for readonly access);
it appears this made it into 1.0.2, currently in beta.
1.0.2 is also planned to add the NON-ephemeral (and non-EC) DH suites. It's not clear if anyone wants or ever used them -- I've certainly never seen any public CA offer DH certs. (Integer DH keys have slightly different encoding than DSA and thus need a different cert, whereas one EC key & cert can be used for either ECDH and ECDSA depending on KeyUsage and technically can be used for both although it is not considered best practice to use one key of any type for multiple purposes.) Adding to otus' correct statement about static-ECDH, static-DH also will not provide PFS.
A more glaring (but non-DH) spelling difference is that OpenSSL names entirely omit "RSA" for plain-RSA key-exchange (not something authenticated by RSA). Also it varies spelling of 3DES. E.g. standard TLS_RSA_WITH_3DES_EDE_CBC_SHA is OpenSSL DES-CBC3-SHA. (Technically EDE is redundant because EEE, the alternative originally considered, was rejected, but putting the 3 after CBC suggests "inner" CBC mode which also was considered but rejected in favor of "outer".)