The symphony had its origins in the overture which was the introductory music for Italian opera?

True!!

The terms "overture", "symphony" and "sinfonia" were widely regarded as interchangeable for much of the 18th century.

The word "symphony" as applied to a composition piece first appeared in the 16th and 17th centuries: i.e. Gabrieli's Sacrae symphoniae (1597), and Viadana's Sinfonie musicali (1610), among many others. Through most of the Baroque period, the terms symphony and sinfonia were used for a range of different compositions, including instrumental pieces used in operas, sonatas, and concertos, as part of a larger work.

By the 18th century, the opera sinfonia, or Italian overture, had a standard structure of three contrasting movements: fast; slow; fast and dance-like. This form is considered the direct forerunner of the orchestral symphony. Symphonies at this time, whether for concert, opera, or church use, were not considered the major works on a program. Often, as with concerti, they were divided up between other works, or drawn from suites or overtures. Vocal music was dominant, and symphonies provided preludes, interludes, and postludes.

The Italian style of symphony was often used as an overture and entr'acte in opera houses, following the three movement form. This was eventually replaced by the four-movement layout that dominated the latter part of the 18th century and most of the 19th century.