For weapons like the spear that have the Thrown property, can a Rogue use sneak attack with them?

Thrown is considered a ranged attack and Sneak Attack specifies that "The attack must use a finesse or ranged weapon."

Does this mean a rogue could potentially apply Sneak Attack to an attack using a spear as it is technically a ranged weapon? If so, would this also work if you were using the spear in melee?

Sneak Attack does not work with melee weapons that have the thrown property, but lack the finesse property

The Rogue's Sneak Attack feature states:

The attack must use a finesse or a ranged weapon.

A melee weapon cannot simultaneously be a ranged weapon, because as the Weapons section (PHB, p146) states:

Every weapon is classified as either melee or ranged.

In fact, a weapon must be listed in either the Simple or Martial Ranged Weapons tables to be considered a ranged weapon.

Moreover, the thrown property (PHB, p146) does not turn a melee weapon into a ranged weapon. It states:

If a weapon has the thrown property, you can throw the weapon to make a ranged attack. If the weapon is a melee weapon, you use the same ability modifier for that attack roll and damage roll that you would use for a melee attack with the weapon. For example, if you throw a handaxe, you use your Strength, but if you throw a dagger, you can use either your Strength or your Dexterity, since the dagger has the finesse property.

Making a ranged attack does not imply using a ranged weapon.

The thrown property allows you to make a ranged attack by throwing the melee weapon despite it being a melee weapon.

Whether or not you throw a melee weapon does not matter. If it lacks the finesse property, then it won't work with Sneak Attack.

No. A thrown weapon is not a ranged weapon for Sneak Attack.

TL;DR: A melee weapon does not become a ranged weapon even if you throw it, nor does it count as a ranged weapon.

This is also discussed in Miniman's answer to the question: "Are weapons with the “Thrown” property considered a “Ranged Weapon” for the purpose of sharpshooter?".

Like Sneak Attack, another class feature that requires a ranged weapon is the Archery fighting style. For that feature, there is a canonical answer regarding whether thrown weapons count as ranged weapons. Per the Sage Advice Compendium, they do not:

Does the Archery fighting style work with a melee weapon that you throw? No, the Archery feature benefits ranged weapons. A melee weapon, such as a dagger or handaxe, is still a melee weapon when you make a ranged attack with it.

So the spear in your example is not a ranged weapon, whether or not you throw it.