A shortbow is recurved in order to give it more pull than its short length would normally grant. Historically, many shortbows were composite, being made of laminated materials like wood and horn. The lamination reinforced the unstrung shape, increase the draw and allowing even shorter bows.
A longbow is a tall, mostly-straight staff of wood that gets most or all of its curve from the tension of the string. The English longbow is the most famous historical example. D&D 3.5e features a composite longbow, though we have no historical examples of such a thing. Both longbows and shortbows can be nocked for free, allowing you to fire and move in the same round.
A light crossbow is about the size of a shotgun. The bow across the stock (hence the name) is relatively small, and constructed like a short composite bow, often made of metal. Because the pull is not too great, light crossbows can be cranked with one hand. The mechanism might be a wheel-crank or a lever, depending on design. In 3.5e, reloading is a move action that leaves your guard down (i.e., it grants adjacent opponents an opportunity attack). This means that the maximum rate of fire is 1/round, and only while mostly staying put (that is, moving at most a 5-foot step).
A heavy crossbow is much more massive and has a heavier pull. To reload it has to be put business-end down while you stick a foot in a stirrup and use two hands on the mechanism to crank the string back. That's what the "2 hands to reload" bit means. In 3.5e, reloading is a full-round action, leaving you unable to do anything else. This makes the rate of fire 1 per 2 rounds at best.
There are advantages and disadvantages to each. Crossbows have longer range, but limited rate of fire. Short- and longbows can take advantage of a Strength bonus to damage, but suffer penalties to damage for low Strength. Crossbows meanwhile are unaffected by Strength, denying a bonus but ignoring penalties.
Crossbows have longer range than regular bows, and though it doesn't matter for a ranger, crossbows also count as Simple weapons which makes them easier to use with less training. Bows count as Martial weapons, limiting which classes may use them proficiently without having to invest feats.
Longbows do triple damage on a critical hit, while crossbows only do double but have a critical-hit range that's twice as large: 19-20 on the to-hit roll, versus just 20 for a bow. Crossbows also do more damage normally, rolling larger damage dice. This loosely represents that crossbows are more hard-hitting than bows, and somewhat mitigates the lower rate of fire.
Shortbows and light crossbows can be used mounted, while longbows can't and, though they may be fired, your DM may rule that heavy crossbows can't be reloaded on horseback.
You must use bows two-handed, while loaded crossbows may be used two-handed with a penalty to hit (that's larger for the heavy variety).
And finally, bows are more iconic for rangers. This may or may not be important to you, though knowing that is useful for mindfully choosing or breaking the stereotype. The issue of what's more iconic also has a slight importance for future magic-item possibilities, as there is more variety of interesting magical bows and arrows than of magical crossbows and enchanted bolts.