How did the design of the hull differ between an Indiaman and a frigate?

There was no standard design for an East Indiaman and, similarly, there was no standard design of frigate, so the exact answer will vary considerably based on exactly which sample vessels you choose to compare. As a general rule, ships of both types grew in size from the start of their development to the end of the Age of Sail. This was mainly due to improvements in materials and technology that allowed longer, stronger vessels to be built.

The first "classic" frigates, i.e. warships with their main battery in a single deck, started to appear around 1750, at which point they were still considerably smaller than the ships-of-the-line that they supplemented and supported. The earliest examples were about 750 tons burthen. A hundred years later, at the time they were replaced by ironclads, these ships had grown considerably, so that the distinction between a large frigate and a small ship-of-the-line was very blurred. As an example, HMS Vernon (built in the 1830s) was just over 2,000 tons burthen, similar in size to a Napoleonic period Third Rate ship-of-the-line.

For Indiamen, their size depended on the roles for which they were used and different sized vessels could be deployed on different routes in the same time periods. For example, the British East India company had different vessels for the China and India routes.

In 1793 the company decided that they should be two classes of ships: 36 ships of over 1000 tons for the China trade, and 40 regular ships of 800 tons for the India trade. In addition there should be ships of smaller tonnage - extra ships - of 500 to 600 tons burthen, employed for several voyages or for a single voyage as circumstances demanded...

^{Lords of the East, the East India Company and its Ships, J. Sutton (1981)}

It's interesting to note that the HEIC's replacement for the classic Indiaman, were much closer in appearance to their naval equivalents. Consequently, they were referred to as Blackwall Frigates (combining the name of the yard where they were built with their style).

In terms of the key differences between the ships, the most obvious arise from their different purposes. The East Indiaman, like all merchant vessels, was designed to carry as much cargo as they could, so their hull cross-sections were deeper and squarer than those of the naval frigates (which only abandoned the traditional tumblehome at the end of the period in question).

In many ways, the larger East Indiaman resembled the smaller ships-of-the-line rather than frigates. The Indiamen kept a double gallery at the stern, which was similar to the style of the two-decker warships. It was this similarity that allowed the HEIC's vessels their finest hour. A fleet of sixteen Indiamen and smaller ships, under Nathaniel Dance, managed to ward off a French squadron under Admiral Linois, largely by bluffing the French into believing that their Indiamen might actually be warships.

There was however a large difference in firepower between the two ship types. The Indiaman carried fewer guns, and these were smaller, lighter and of a lower quality compared to those of a warship. The smaller crew carried by the merchant ships also meant that their guns had a lower rate of fire so they were far from a match when it came to battle.

In terms of construction, the methods of construction were very similar. This shouldn't be too surprising as many shipyards built vessels for both the navy and merchant fleets. Naval vessels were the first to adopt coppering to keep their hulls clean but when the advantages were seen the Indiamen were similarly sheathed.

In other areas, the Indiaman were technologically ahead. For example, during the long period of the French Revolutionary & Napoleonic Wars, demand for timber for ship building was at a height. As the Navy were given priority on timbers, the builders of the East Indiamen were driven to use metals to replace timber in key areas, such as the knees and brackets. This actually improved the strength of these joints and this construction was subsequently introduced into the warships.