Non-pedal/lever/folk Harps
Folk harps include a wide variety of harps that do not use pedals to change the pitch of the strings. Many use levers (see the two harps on the left in the image above) to change the strings by one half note (ex. with the lever down, the string is an F, with the lever up, the string is now a F#). Strings may be made of gut, nylon, synthetics, or wire. Wire-strung harps are played with the nails instead of the fingertips. Nylon, gut, and fluorocarbon strings are the most common; are larger folk harps will usually have some metal strings for the lowest notes. Harps may be lap sizes (22-26 strings), mid-size (26-29 strings with a base that brings the harp to playing height) or floor harps (32-38 strings).
Advantages: more portable (~10-30 lbs), more affordable, lighter string tension is ideal for playing ornaments commin in Celtic music, many choices of makers in the US.
Disadvantages: not suited for most orchestral and jazz music since you have to manually flip a lever on each string separately to change key, making rapid changes too big a challenge in most cases. The folk harp also can't play in any key, but as long as you aren't playing with someone else, there is often a way to set your levers to still play the piecde, just one half step lower or higher.
Sheet music is usually marked for harp or pedal harp only and will indicate if it's lever-friendly (for "all harps" or "for lever harp").
What to avoid
If you are searching for a harp, please avoid the majority of harps on ebay which are from Pakistan (watch out for harps with lots of duplicates, carved rosewood, Deura). One exception are harpsicles, which do often appear on ebay but are quality instruments made by Rees Harps in Indiana. Note that the base harpiscle model can never have levers added, so it can only play in one major key; if you want levers, look for "sharpsicle, flatsicle, or fullsicle" models. Before buying an instrument, please consult with a harp teacher or experienced performer who can assist you.
Pedal Harps (see harp on right)
Pictured above: lever harp on the left, pedal harp on the right
Pedal harps have 7 pedals at the back (at the bottom of the harp), one for each string in the scale. In a modern pedal harp, each pedal has 3 positions, for flat, natural, and sharp. If you see a single-action pedal harp, that means each pedal only has two positions.
Advantages: more strings (44+), easily play in any key, play almost any harp music, including orchestral scores and jazz, more types of glissandos. Higher tension strings are ideal for fast notes in the base without sounding muddy
Disadvantages: more expensive, heavier, and harder to transport (may also require a certain size vehicle to transport)
Many pedal harpists started their harp adventure on a lever harp. The technique should be the same or similar, and there are lever harps with higher tension strings that make an excellent bridge from lever to pedal harp. Folk harpists would note that this is not "trading up" however. Both lever and pedal harps are performance instruments and are unique in their sound and capabilities.