Spellcasting of this wizard/loremaster
You have the spellcasting of a 13th-level wizard.
When a new loremaster level is gained, the character gains new spells per day (and spells known, if applicable) as if she had also gained a level in a spellcasting class she belonged to before she added the prestige class.
Thus, at ECL 12th, you have the spellcasting of a 12th-level wizard. You are a 12th-level wizard—for the sake of spells per day and spells known. When you gain another level of wizard at ECL 13th, therefore, and you determine your new spells per day (and spells known), you are a 12th-level wizard advancing to 13th, and gain 7th-level spell slots for the first time.
Just to confirm this, loremaster continues by saying
This essentially means that she adds the level of loremaster to the level of some other spellcasting class the character has, then determines spells per day, spells known, and caster level accordingly.
By using the verb “adds,” this sentence makes it clear that the order of loremaster and wizard levels doesn’t matter—addition is commutative, so 9 + 3 + 1 = 9 + 1 + 3 = 13.
For other class features—familiar and bonus feats—you are not a 12th level wizard advancing to 13th, you are a 9th-level wizard advancing to 10th. You therefore get a bonus feat, as normal for the 10th level of wizard, and your familiar gets that much closer to its next advance.
Broader questions about prestige class spellcasting advancement
I will caveat here, however, and warn that the spellcasting blurb of various prestige classes are not always the straight copy-and-paste you would expect them to be; they sometimes use different wording for what appears to be the same feature. I strongly suspect that it had more to do with word-count—maximizing it for the sake of pay, minimizing it for the sake of fitting in the book—than it did with the actual rules. And not all of the wordings are equally clear or thorough.1
I strongly recommend that you ignore all of that. These are slight differences in wording with little to suggest that they were intentionally having one prestige class work subtly differently from another. There is no rhyme or reason to which one is which. And as a sometime d20 System author (for a third-party publisher in Pathfinder 1e, a spin-off of D&D 3.5e), I am absolutely certain that the authors were not carefully considering their options with any of these things.
Instead, the only things from the spellcasting blurb that should matter are
- the levels at which the class advances your spellcasting,
- requirements like arcane or divine on the chosen spellcasting class(es).
Otherwise, every PrC should advance caster level, spells per day, and spells known, and should allow you to mix and match which classes you advance with each level, and should allow you to choose classes you only got levels in after first entering the prestige class. There just is no good reason to limit any of those things—and the sheer coincidence of the wording the author chose to use is absolutely a bad reason to do so.
For more on this subject, see this Q&A.
- For example, the first sentence of the loremaster version doesn’t mention caster level—even though the later sentence says the first “essentially means” to include it. Likewise, some prestige classes leave out spells known. There are also differences about how the choice about which spellcasting class to advance is made, in the case where you are a multiclass character that already has multiple spellcasting classes the prestige class could advance. Sometimes tells you to choose one class when you first enter the prestige class, and all the prestige class levels advance that one. Others tell you to choose separately for each level of the prestige class. Some of those say the chosen class must be one you had levels of before you first entered the prestige class; others allow you to choose any class you had levels of before that level.