"+1 level of existing divine spellcasting class"

[NOhara24]

I'm looking into Prestige Classes for a couple characters, and in the "Spells per day" column, it lists "+1 level of existing divine spellcasting class". I'm not quite sure how to interpret that.

Say that I'm a Paladin 6/Gray Guard 2, would I have spells available to me as if I were a level 7 paladin? Or do I take another level in paladin upon getting to gray guard 2?

[Claudius Maximus]

The former. You just get casting:

Spellcasting: At each even-numbered level, you gain new spells per day and an increase in caster level (and spells known, if applicable) as if you had also gained a level in a divine spellcasting class to which you belonged before adding the prestige class level. You do not, however, gain any other benefit a character of that class would have gained.
Emphasis mine.

[gbprime]

The former. You just get casting:

Emphasis mine.

In short, yes. Level 2 of Gray Guard makes your casting the equivalent of paladin 7. And level 4 makes it paladin 8, etc.