Generally, you discover something that is natural, something that already exists.
You invent something new, something that has to be made, manufactured, following a series of steps, procedures.
Develop is similar to invent, but it stresses that it's a complicated process, with experimentation, trial-and-error.
Penicillin was discovered by accident, when a scientist left a dish uncovered.
The transistor was invented to take the place of vacuum tubes.
Scientists are working to develop a vaccine for AIDS.
English speakers are sometimes careless about these distincitions--I've heard electricity referred to as an "invention." Electricity was a discovery, not an invention. The electric light bulb was an invention. The system for distributing electricity across continents was developed.
wishing you success
- For Teachers