The sherwani and the achkan are both long coats worn over the churidar and kameez for formal occasions. Both have a standing collar, a front closure and a hem at or below the knee. Confusing them is entirely reasonable. But they're built differently, decorated differently, and they belong at different kinds of function, and if you're commissioning one it's worth knowing which you've asked for.
How each one is built, and why it matters
The achkan is the more tailored of the two. It uses canvas and chest interfacing much like a Western coat, which gives it a shape it holds on its own from shoulder to hem. The sherwani is usually built with less internal structure and leans on the body of the cloth, brocade or velvet especially, to keep its form. So the achkan reads as architectural and precisely cut, the sherwani as rich and ornamental.
Embellishment follows the same split. The achkan carries less embroidery and relies on its construction and its cloth to do the work, with anything applied kept restrained: a border at the collar and cuffs, perhaps a small motif at the chest. The sherwani far more often puts heavy or all-over embroidery front and centre and makes that the point of the garment.
Which one to order for your occasion
Choose the sherwani when the occasion is at its most ceremonial and visual richness is called for: the groom's own coat, a major religious function, a state occasion where Indian dress at full strength is expected. The embellishment and the cloth carry the message that this is the biggest day on the calendar.
Choose the achkan when you want the authority of a long coat without the ornament: for a groom with a quieter eye, for a father or brother who wants to be very well dressed at the wedding without approaching the groom's level of decoration, or for any formal occasion where the tailoring rather than the embroidery is meant to be the point. In fine raw silk or a good suiting wool, with no work on it at all, an achkan is one of the most quietly impressive things a man can wear.