yes they do but there thrust can be controlled by the guiding system on board as for solid fuel once fired cant be stopped only to self-destruct if some thing goes wrong
both liquid and solid fuel
rockets/missiles have there own advantages and disadvantages.
Solid-fuel Rockets advantages
Very stable, durable
More thrust for a similar size rocket
Solid-fuel missiles disadvantages
Can't be turned off- once the burn starts, it goes until fuel is used up
Fuel decomposes, must be replaced.
Liquid-fuel missile advantages
Variable thrust- the amount of fuel and rate of burn can be changed in flight
Liquid-fuel boosters are more easily re-usable
Liquid-fuel missile disadvantages
Fragile, many complex parts
Oxidiser (liquid oxygen) must be kept extremely cold.
Solid propellant rockets are much easier to store and handle than liquid propellant rockets. High propellant density makes for compact size as well.
These features plus simplicity and low cost make solid propellant rockets ideal for military applications.
Their simplicity also makes solid rockets a good choice whenever large amounts of thrust are needed and cost is an issue.
The Space Shuttle and many other orbital launch vehicles use solid-fueled rockets in their boost stages (solid rocket boosters) for this reason.
A drawback to solid rockets is that they cannot be throttled in real time, although a programmed thrust schedule can be created by adjusting the interior propellant geometry. Solid rockets can be vented to extinguish combustion or reverse thrust as a means of controlling range or accommodating warhead separation.
Relative to liquid fuel rockets, solid fuel rockets have lower specific impulse.
Liquid fueled rockets have higher specific impulse than solid rockets and are capable of being throttled, shut down, and restarted. Only the combustion chamber of a liquid fueled rocket needs to withstand high combustion pressures and temperatures and they can be regeneratively cooled by the liquid propellant. On vehicles employing turbopumps, the propellant tanks are at very much less pressure than the combustion chamber. For these reasons, most orbital launch vehicles use liquid propellants.
The main difficulties with liquid propellants are also with the oxidizers. These are generally at least moderately difficult to store and handle due to their high reactivity with common materials, may have extreme toxicity.
Liquid fueled rockets also require potentially troublesome valves and seals and thermally stressed combustion chambers, which increase the cost of the rocket thus not good for military use!