*flagged to be moved to Pathfinder First Edition Rules Questions*
Caster level mostly differs from class level when you are multiclassing. For example, a fighter 5/wizard 3 has a class level of 8 but a caster level of 3. A cleric 4/ wizard 2 has a class level of 6, a cleric caster level of 4 (used when casting divine spells: so cure light wounds would cure 1d8+4 points of damage), and a wizard caster level of 2 (used when casting arcane spells, so there would be one missile when casting magic missile). Some prestige classes, such as mystic theurge, advance both divine and arcane caster levels with each level taken, as a special feature.
As to your question about the Eldritch Blade exploit, I too was momentarily flummoxed. If you are a single-class Blade Adept Arcanist, then, yes, your class level and your caster level should be the same. This thread sheds some light on the subject, however.
It's primarily to allow Arcanists who take it to take prestige classes like Eldritch Knight or Hellknight Signifier and progress their Black Blade at the same time. Because let's face it, you're not going to be using that sword any time soon if you stick with a 1/2 BAB class.
It's an exploit you can choose to take if you intend to multiclass to keep your black blade relevant.
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Okay, let's see, under Common Terms, we have:
Caster Level (CL): Caster level represents a creature’s power and ability when casting spells. When a creature casts a spell, it often contains a number of variables, such as range or damage, that are based on the caster’s level.
and
Level: A character’s level represents his overall ability and power. There are three types of levels. Class level is the number of levels of a specific class possessed by a character. Character level is the sum of all of the levels possessed by a character in all of his classes. In addition, spells have a level associated with them numbered from 0 to 9. This level indicates the general power of the spell. As a spellcaster gains levels, he learns to cast spells of a higher level.
So, caster level is only for casters, class level is per class, and character level is the total of all class levels each character has. A 7th-level wizard would be a 7th-level caster, 7th-level wizard, 7th-level character, but a fighter 5/wizard 3 would be a 3rd-level caster, 5th-level fighter and 3rd-level wizard, and 8th-level character.
For non-full casters (paladins, rangers, etc.), your caster level is defined in your class write-up as a certain number of levels lower than your character. E.g., "Through 3rd level, a paladin has no caster level. At 4th level and higher, her caster level is equal to her paladin level – 3." So a paladin 4/bard 2 would be a 1st-level caster as a paladin and 2nd-level as a bard, a 4th-level paladin and 2nd-level bard, and a 6th-level character.
And a cleric 3/wizard 3/mystic theurge 2 would be a 5th-level divine caster and 5th-level arcane caster, a third level cleric, third-level wizard, and second-level mystic theurge, and an 8th-level character.
MEA CULPA: I misspoketyped in my previous post, conflating character level with class level, but it's too late to edit. All the various kinds of levels always get me thinking of this. :P
The Character/Class level confusion aside, given the scenarios presented I still don't see an explanation for the scenario of how class and caster level behave when a character multi-classing for spells from the same type (ie Arcane) or classes with spells from the same spell list occur.
For example if a character multiclasses as a Sorcerer lvl 3/Magus lvl 2 and they cast Magic Missile, which both classes have, but in different spell lists do they have to specify that a particular version of magic Missile is being cast? Those versions being the Sorcerer caster level 3 version or the Magic caster level 2 version?
Yes. Spell slots and lists remain separate. If you're a wizard 5/sorcerer 2, you would have a certain number of spell slots you're filling by memorizing spells out of a spellbook and another number you're spontaneously casting out of your sorcerer spells know. In that case, a magic missile prepared and cast as a wizard would give you two missiles, and one spontaneously cast as a sorcerer would only have one (because of your different caster levels).
Here's a thread about multiclassing arcane classes.
On the Magus spell list I found the following definition of caster level
https://www.d20pfsrd.com/magic/spell-lists-and-domains/magus-spell-listCaster Level: A spell’s power often depends on caster level, which is defined as the caster’s class level for the purpose of casting a particular spell. The word “level” in the short spell descriptions that follow always refers to caster level.
Based on this definition if Class level meant character level, that wouldn't make much sense to me, because then you could go into Marshall classes to benefit caster level on spells.
Caster level = "class level for the purpose of casting a particular spell," not just caster level = class level *fullstop*. If it's a spell on the magus spell list, then your caster level is your magus level; having fighter levels (or cleric levels or bard levels or wizard levels) doesn't affect your ability to cast a spell on the magus spell list.
On the otherhand if class level is simply in reference to a single class why is there a distinction at all between caster level and class level when it comes to spell casting?
Because if you're a paladin or ranger 6, your character level is 6, your class level is 6, but your caster level is 3.
Joana's 2nd post (and those following) has it basically right (including the linked Order of the Stick page), but just to confuse you even more, certain abilities allow you to boost your caster level (often temporarily) beyond beyond the class level of the class providing your spellcasting (or even beyond the sum of this with prestige class levels that boost the same spellcasting progression), and innate spell-like abilities can progress with character level (for creatures with only class levels) or with total hit dice (for some other creatures) or even have set values (for some other other creatures), with spell-like abilities from Variant Multiclassing potentially emulating any of the above (possibly with a negative offset). And now that Pathfinder 2nd Edition is out (and it's REAL EASY to get confused about which edition the thread you are in is for), this has its own way of doing multiclassing that is different from Pathfinder 1st Edition.