Capacity looks a little bit like the English word "capable", so capacity means how much something can support, lift or hold: a floor can support X number of pounds/kilograms or a crane can lift X amount of weight or a tank can hold X litres of fluid. Parameter means something (a factor or characteristic) that can be measured. "...meter" means measure, like a thermometer is a meter to measure the thermal energy (heat/temperature). For example, a spaceship has many parameters that must be measured, such as speed, strength, temperature, pressure, direction, fuel, etc.

In the mechanical field, the term parameter is quite often used to mean capacity. A major part of mechanical engineering is determining the load capacity of a given material, connector (e.g. screw, bolt, pin, etc.) or machine part. Because this is such an important issue, quite often the first thing that someone in the field thinks of when asked "What are the paramenters of use?" is the load capacity. But it is definitely not the only parameter that person would think of. As was said by Richard, they are clearly not the same. Parameters include so much more than load capacity, in fact it includes all of the different factors which can be measured which impact efficient use. The list can be endless and capacity is just one of the items.

These two words aren't even remotely similar. Ah.