Rosin comes in a variety of formulas to suit different instruments, playing styles, and climates.
Light rosin is harder and less sticky, good for use in warm and humid playing environments while a dark rosin is softer and stickier, working best when it's cool and dry. Violin and viola players tend to use a harder rosin, cello players a medium rosin, and the softest, stickiest rosins are used by bass players for the extra adhesion and grip on thick strings.
Some rosins contain particles of precious metals, like gold, thought to provide tonal benefits as well as increase static friction for clarity of articulation. Other rosins are made with pure formulas with no metal additives for a smooth and silkier feel. There are many "secret" formulas for making rosin that rosin producers tend to protect.
For players sensitive to the dust that rosin creates, there are hypoallergenic rosins that produce little to no rosin dust and leave little to no residue on the instrument.
Light movement of your bow across the cake of rosin 4 or 5 times is usually enough to do the job. Many new string players use too much rosin creating a bit of a mess as they play! If your bow has never before had rosin on it you may need to spend a little more time with it. Sometimes a cake of rosin will need to have the surface "roughed" up a bit for a good transfer of rosin to the bow.