The sonnet is a poetic form that is thought to have been developed in Italy by the 13th century poet Giacomo da Lentini. A sonnet is defined by several requirements, the first of which is that it is fourteen lines in length. In addition to that, the sonnet follows further conventions, including structure and rhyme scheme, depending on what type of sonnet it is.
The Italian sonnet (also known as the Petrarchan sonnet after Franceso Petrarca) can be considered the 'original' form of the sonnet. The basic structure of an Italian sonnet is that it can be divided into two parts. The first part of the poem often introducing a problem or argument, and was eight lines long (an octet- or two quatrains). The rhyme scheme convention for these initial eight lines was a-b-b-a a-b-b-a. On the ninth line the poem marks a shift or turn, known as the volta, which leads into the second part of the poem, and presents an answer or resolution to the first part. This second part is six lines long (a sestet- or two tercets). The convention on rhyme scheme for the second part of an Italian sonnet is either c-d-e-c-d-e or c-d-c-c-d-c, although other variations did emerge.
The development of the English sonnet from the Italian can be attributed to The Earl of Surrey Henry Howard who introduced conventions of rhyme, meter, and the structural division into three quatrains and a final couplet that differentiates the English sonnet. The meter employed in the English sonnet (with few exceptions) is Iambic Pentameter. The rhyme scheme used is usually a-b-a-b c-d-c-d e-f-e-f for the three quatrains, and is then finished with a g-g- rhyme for the final couplet. This type of sonnet is also known as the Shakespearean sonnet, in tribute to William Shakespeare's considerable contributions to the form.
So, to answer your question, the principal difference between the two sonnet forms can be seen in both meter and rhyme scheme, as these are two elements of the sonnet that developed with the forming of the English sonnet convention.