D&D 5E Expanded Spell lists?

I have a question on expanded spell lists:

I know the expanded spells don't count against your "known" spells.

But what I want to know is do they count against your spells cast for the day? So if you have the ability to cast 2 level 1 spells and you have an expanded spell from a class feature and use a 1st level spell from it, does it use up a daily use? Or is it class dependent?

I know the Cleric and the Warlock are examples of these expanded spell lists.

Thanks in advance!

You still use an appropriate spell slot to cast those spells.

Each thing that provides these spells that you refer to as "expanded spells" tells you what it does or does not count as:

For example, cleric domain spells are spells which are always prepared but do not count against your level + wisdom modifier prepared spell limit - and do not say they are cast without spell slots, so you must still follow that general rule of a spell slot being spent to cast them.

Yet warlocks have different types of expanded spells: they have their pact "expanded spells" (the only place that actually uses that phrase, as far as I know) which are only added to the list from which known spells can be chosen (they are not inherently learned or prepared), and they also have invocations like Armor of Shadows that allow them a spell that does not use spell slots and like Dreadful Word that do use a spell slot to cast the granted spell and are also limited in how often that casting can be done.

Plus, there is the case of the Magic Initiate feat which gives knowledge of a spell and also a once per day casting that doesn't use a spell slot, but can be cast with spell slots if the character taking the feat fits the correct circumstances (i.e. a sorcerer taking the feat and choosing spells from the sorcerer list for its benefit).