Does the different capsid morphology shapes each have a different function along with the different shape or is the only difference between them the shape?

Capsid shapes are only different and all different shapes have same function.

Explanation:

A capsid is the protein shell of a virus  that encloses the nucleic acid; with its enclosed nucleic acid, it is called the nucleocapsid. This shell is composed of protein organized in subunits known as capsomers. They are closely associated with the nucleic acid and reflect its configuration, either a rod-shaped helix or a polygon-shaped sphere.

Helical – These viruses are composed of a single type of capsomer stacked around a central axis to form a helical structure, which may have a central cavity, or hollow tube.

Icosahedral – Most animal viruses are icosahedral or near-spherical with icosahedral shaped capsid.

Complex – These viruses possess a capsid that is neither purely helical nor purely icosahedral, and that may possess extra structures such as protein tails or a complex outer wall.

The capsid has three functions:

1) it protects the nucleic acid from digestion by enzymes,

2) contains special sites on its surface that allow the virion to attach to a host cell, and

3) provides proteins that enable the virion to penetrate the host cell membrane and, in some cases, to inject the infectious nucleic acid into the cell's cytoplasm.

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