So, Eldrich blast being a cantrip is separate from the five Warlock spells, or is it part of the five spells?
So divine smite, is part of the four Paladin spells?
So what your saying, is that the Warlock spells are more economical to use. I would need a long rest to be able to use say use Cure wounds again.
Where as a Warlock, I would only need only to rest 10 minutes(Short rest?). Then be able to use hold person again.
Assuming all five slots are taken up, and ready to go.
Please take another look at the player's handbook, all of this information is detailed in there.
-You should have 3 warlock cantrips, no they're not included in the 5 spells mentioned before. You can cast cantrips all day long without spending slots.
-A short rest is 1 hour long, not ten minutes.
-Divine smite is a Paladin class feature, not a spell. It lets you sacrifice spell slots in order to do more damage with a melee weapon.
-Warlock spell slots are in theory more efficient, but you do only have 2 slots, and you are not guaranteed to get the chance for multiple short rests in a day.
-You can cast paladin spells with warlock slots, and vice versa.
Eldritch blast is a cantrip. It doesn't count against your warlock slots. You can cast it every turn all day every day. Smite is a paladin spell. You are correct about the economy. Once a paladin spell slot is used it's gone until after a long rest. Warlocks get their spell slots back after a short rest which is an hour now. You get two warlock spell slots. After a short rest you have the two spell slots again. You might know more spells than that but you only have two slots per short rest for warlocks.
Yes do not confuse spells known/prepared with the slots. The slots could each be used to cast cure wounds several times before the next rest, choosing that over other spells. Alternatively they could all be used to fuel smites (A class feature, not a spell) instead of spells. Any combo of this is fine, slot level and spell level dependent, of course. It is not a fixed “this spell slot is prepared with cure wounds for today” spell / slot relationship.
As Daishain said, probably worth a read of the Spellcasting section of the Player Hand Book as well as the spellcasting section for each of your classes since they are very different.