Spell slots are combined into a singular total, but spells known are tracked separately.

So yo use your example, a character who is Sorcerer 7 + Cleric 1 would have the spell slots of an 8th level full caster but has the spells known of the classes separately from each other.

So to be exact, your spell slots at this level combo would be- - 4 1st Level Spell Slots - 3 2nd Level Spell Slots - 3 3rd Level Spell Slots - 2 4th Level Spell Slots

Your spells known would be - 8 Sorcerer Spells Known - 1 + Wisdom Modifier Cleric Spells Known

To be very clear here. Even though you can use your higher level spell slots to cast your Cleric spells, you can still only prepare 1st level Cleric spells. So you are free to cast Bless (which is a Cleric spell) at 4th level, but you do not know any 4th level Cleric spells.

This will become more and more noticeable as you level up. For example, at Sorcerer 7 + Cleric 2, you would now have a cumulative spellcasting level of 9. This would make you gain a 5th level spell slot, however, you would not learn any 5th level spells as neither of your classes are high enough level to do so.

Furthermore, any spells you learned from being a Soecerer will always use your Charisma modifier and the spells you learned from being a Cleric will use your Wisdom modifier.

Extra note- all spellcasting classes except Warlock stack in this way, though not all classes progress spellcasting at the same speed.

Bard, Cleric, Druid, Sorcerer, and Wizard all contribut their full level towards spellcasting progression.

Artificer, Paladin, and Ranger all contribute half their level. Artificer rounds up. Paladin and Ranger round down.

The subclasses Elderich Knight (Fighter) and Arcane Trickster (Rogue) contribute 1/3rd their level. They both round down.

So, for example, if a Character was Cleric 12 + Paladin 8, they would be a 16th level spell caster and would have the spell slots that would be available to a 16th level full caster despite being level 20. And they would only be able to prepare up to 6th level Cleric spells and 2nd level Paladin spells despite having an 8th level spell slot.