The biggest difference between ghosts and spectres are ghosts are unfettered spirits on the Ethereal Plane, while Spectres are damned undead spirits on the Negative Material Plane. Ghosts also age anyone who sees their true form, while spectres immediately seek to drain life levels from the living.
It's understandable that ghosts sound like they should be weak challenges in D&D as they are very prevalent in mythologies across the world. The 4th playtest packet with Ghosts as worth only 80 XP backs this up. The AD&D Monster Manual ghosts were amongst the most serious undead threats one could face. I see them as evil, unforgiven spirits no god wanted. The souls of the unbelieving damned left to haunt the world. Spectres are part of the negative energy, level draining undead that make up most all of the rest.
Here's the Turning Table from 1e:
- Skeleton
- Zombie
- Ghoul
- Shadow
- Wight
- Ghast
- Wraith
- Mummy
- Spectre
- Vampire
- Ghost
- Lich
- Special (demons, devils, etc)
D&D ghosts are not quite those from mythology. It's more of a game term for a specifically defined type of creature, just like kobold or goblin.
Ghosts first seek to possess enemies when non-material and invisible. If this strategy ultimately fails (perhaps they try more than once), then they manifest into semi-material transparent spirits of unlife. They are so hideous anyone viewing them is aged 10 years and panicked for about 1 hour (aging is one time only) and any they touch by them when manifested ages victims 10-40 years. Obviously conversing in this state isn't exactly ideal. Bright light will cause them to flee or dematerialize however.
Ghosts roam nightly, are tied to one place or thing, and are only active when it's dark. They are almost always alone and any treasure they have is (almost always) guarded-only material. Any creature aged to death by a ghost is "forever dead" as its soul joins those lost on the Ethereal plane. (Perhaps a quest into the ethereal realm to send this spirit to its deity & then resurrect the soul or raise its body could work however, but that would be quite dangerous)
Ghosts are immune to normal weapon and the prime material world at large, even when manifested. However, silver will harm them for 50% damage and magic weapons harm them normally (as I would guess force effects do as well). Magic spells only effect ghosts if the caster of the effect is ethereal (incorporeal) or fully on the Ethereal plane.
Spectres are incorporeal undead souls nearly completely made up of negative energy, the plane upon which they live. They do not materialize, but are always manifested between realms, haunting only dark places as light (positive energy) can destroy them. They hate sunlight and all living things, so while it may have a lair it frequently moves leaving a path of death in its wake. Due to these effects, these creatures tend to live in ony the most desolate of locations, like tombs and undead filled dungeons.
Spectres attack like wraiths, but are more powerful doing 2 levels of draining per attack. However, they are a negative energy creature in semi-materialized state, so their attacks also harm victim's bodies for 1d8 hit points.
Spectres are "True" undead having their power come from negative energy. Therefore they are immune to mind affecting spells (like hold, charm, and sleep) & all cold-based spells (note, they can be burned). They are immune to poison and paralysis, but susceptible to holy damage like that from holy water. A Raise Dead spell can destroy them, if they fail their save (their negative energy-infused bodies are beyond being raised, but perhaps a resurrection may work, once they are destroyed.)
For my own take, I'm thinking Spectres are similar to Ghasts as Wraiths are to Wights. But I don't see anything in D&D history for that connection either.