First, the Epic Level Handbook isn't necessarily wrong, but it does weasel mightily: It says that the "following are typical characteristics of an epic magic item[, and, i]n general, an item with even one of these characteristics is an epic magic item" (123). Then it goes on to list a magic item that provides "an enhancement bonus on a skill check greater than +30" as one possible typical characteristic (ibid.). Here the Epic Level Handbook is leaving things to the DM while still providing some guidelines. Now, while this is an awfully apologetic stance to take on what's been referred to by wiser and more ardent fans than I as the D&D Joke Book, magic item design broadly really is less hard-and-fast rules and much, much more guidelines, and the DM's given these guidelines so the game can be extended beyond what's already there. This should be clear upon realizing that not one single magic item in the Epic Level Handbook actually grants a +31 or higher enhancement bonus on skill checks!
With that out of the way, let's talk bonuses.
Magic items can grant any kind of bonus the DM permits them to grant
One of the things that the game tacitly encourages is bonus-scrounging: Dumpster-diving for bonuses that either have different names or are unnamed and come from different sources.1 An industrious player with a full bookshelf can find himself with a very big pile of differently named bonuses and unnamed bonuses that're from different sources, all stacking to improve his PC's most important feature.
So, yeah, magic items that grant enhancement bonuses on skill checks exist like the Epic Level Handbook says, magic items that grant competence bonuses on skill checks exist like the Dungeon Master's Guide says, and magic items that grant circumstance, insight, divine, and unnamed bonuses on skill checks exist, too. They're all there somewhere, existing in relatively harmony, and all the different ones (or unnamed ones from different sources) can stack if the consumer is careful in his purchases.
The DM, however, runs the game, and—among other responsibilities, obviously—the DM decides two important things:
- The magic items that are available in the campaign.
- The price of any new magic item proposed by a player.
This means that there's no guarantee that a specific magic item is available in a specific campaign (although many, many general magic items should be readily available lest the PCs die frequent, horrible, ignominious deaths), and this means that if a player pitches a new magic item, the DM picks the price by comparing it to existing items, and, if he doesn't like the magic item, he can (although he shouldn't) passive-aggressively price it through the roof, or (more appropriately) he can just say No.
Thus, while I'm certain such items exist in the vast Dungeons and Dragons 3.5e corpus, I'm unaware, offhand, of a lone magic item that grants a creature two or more differently named bonuses to the same feature. For example, I'm unaware of a lone magic item that grants both a +10 competence bonus on Tumble skill checks and a +10 enhancement bonus on Tumble skill checks. That's something that, for whatever reason, the game just doesn't do with any regularity. A lone magic may grant different bonuses to different features—that's not particularly rare. And two or more different magic item can be combined into a lone magic item to provide different bonuses to the same feature, but such an item's usually the result of an owner having paid a premium to combine the different magic items.2
In other words, if you're a new player who's trying to figure out all the bonuses you can get to a specific skill, rather than trying to design wholecloth a custom item and get it approved by the DM, it's usually better to find a published item like the one you want and work from there. And if you're a new DM, and your players are clamoring for a dozen, dirt cheap magic items that each grant a differently named +2 bonus on Use Magic Device skill checks or whatever, you can ask to see similar items to the ones they're proposing and price the items appropriately or you can just say No.
1 My answer here on how to improve Spot skill checks, for example, does exactly this, as does my answer here on how to improve speed. (Don't judge! I like research.)
2 For more information see Magic Item Compendium on Improving Magic Items (233-4).