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I'm a bit confused by the text for damage reduction. It is stated that:
DR 5/magic means that a creature takes 5 less points of damage from all weapons that are not magic. If a dash follows the slash, then the damage reduction is effective against any attack that does not ignore damage reduction.
That would mean that DR/magic counts for all magic weapons to ignore the DR. But DR/- sounds like only ignoring weapons count there.
Am I wrong there, or what is really meant?
Yes, DR X/- is only negated by attacks that ignore damage reduction.
DR of the X/- kind is generally the most powerful kind of damage reduction you can get, because there's almost no kind of direct physical damage that overcomes it. However, you should remember that some kinds of damage - most usually energy damage, like that from a lightning bolt or the extra damage from a flaming sword - are never affected by damage reduction:
Damage Reduction does not negate touch attacks, energy damage dealt along with an attack, or energy drains. Nor does it affect poisons or diseases delivered by inhalation, ingestion, or contact.
Magical spells also usually bypass damage reduction, unless the damage they deal is specifically typed as physical damage - any damage called out as slashing, piercing, or bludgeoning must contend with the target's DR.
There is, however, one circumstance in which DR X/magic might be better than DR X/-. Creatures with /magic damage reduction have their natural weapons count as magical:
Some monsters are vulnerable to magic weapons. Any weapon with at least a +1 magical enhancement bonus on attack and damage rolls overcomes the damage reduction of these monsters. Such creatures’ natural weapons (but not their attacks with weapons) are treated as magic weapons for the purpose of overcoming damage reduction.
A few very powerful monsters are vulnerable only to epic weapons—that is, magic weapons with at least a +6 enhancement bonus. Such creatures’ natural weapons are also treated as epic weapons for the purpose of overcoming damage reduction.
DR X/- offers no such advantage.
DR works like a “whitelist”—it tells you what damage it allows through, and it blocks everything else. So DR \$x\$/magic reduces damage by \$x\$, but not if the attack is made with a magic weapon. And DR \$x\$/– is an empty whitelist—it doesn’t allow anything through, it just reduces attack damage by \$x\$ unless the attack has extra-special ability to overcome DR (as with a paladin’s smite evil).
As a result, we can draw some conclusions about the potency of each form of DR:
DR \$x\$/magic is basically worthless past about 5th level. Every serious threat that is trying to hit you with physical attacks has a magic weapon that ignores that DR (creatures who have DR \$x\$/magic themselves count their natural attacks, like claws, as magical for overcoming DR, so even most beasts ignore it). You (or a monster) could have DR 1,000,000/magic and it wouldn’t matter at all after the lowest levels in the game.
On the other hand, DR \$x\$/– is not ignored by any physical attacks at all. All weapons will have their damage reduced when attacking DR \$x\$/–. In principle, that makes DR \$x\$/– very good, because it is perfectly reliable—any time you are subject to a physical attack, it applies.
However, in practice, DR \$x\$/– is also very low-value for players. Quite simply, you can never find high enough \$x\$ values to make a large difference, and the cost of getting what you can is far too high for the small difference they make. Pathfinder charges a lot (in terms of feats, class levels, gold, etc.) for even tiny amounts of DR \$x\$/–.
Ultimately, DR is much more the province of monsters than it is players. Monsters come with DR, often DR \$x\$/material or DR \$x\$/alignment, that is large enough to matter, without necessarily having to “pay for it” the way players do. Some even get decent chunks of DR \$x\$/–.
Note, however, weapon enhancement bonuses can overcome material-based and alignment-based DR. Monsters having that DR still matters, unlike the DR \$x\$/magic, though, as the existence of those DR values strongly encourages players to get those enhancement bonuses instead of special weapon abilities (unlike D&D 3.5e, where enhancement bonuses are basically a waste of gold and no one should ever get more than the minimum +1). So such monsters are “protected” from more powerful weapons by forcing players to get the (otherwise-weaker) straight enhancement bonuses.
At the highest levels of the game, though, DR \$x\$/– is the only form of DR that will actually come into play. It’s still usually too small to make a big difference, but some monsters are exceptional in that regard.
Finally, keep in mind that DR, even DR \$x\$/–, only ever applies to physical attacks. Magic energy attacks and the like don’t interact with DR at all. Resistance and immunity are similar concepts that apply to magic (and not physical attacks). However, resistance is a blacklist system, as opposed to DR’s whitelist system (that is, resistance tells you what it blocks, and it doesn’t block anything else; DR tells you what it doesn’t block, and it blocks everything else).
