As far as I know:

Most of the active ingredients in mj are produced in tiny resin glands called trichomes. You can knock the trichomes off in various ways - sifting, water process, whatever. You take your collected trichomes & press them into a solid mass - that's hash.

OR you can use various chemical solvents - butane & alcohol are the most popular - to melt the trichomes. Then the solvent is evaporated out, & the remaining resin is called, you guessed it - hash oil.

Good BHO (butane hash [or honey, for the color] oil) is generally reckoned to be strongest & purest mj preparation most people are likely to come across. It can also be a royal pain in the ass to deal with, as it's essentially a little blob of tar.

I hold no brief for either; I am a tincture devotee.