Why is a Galaxy a flat disc while a globular cluster is a sphere?

Question

This has been bugging me for some time now?

Answer 1

Disks occur astronomically when a system collapses collisionally. The frequent collisions between the particles allow exchange of energy and momentum. The result is nearly complete gravitational collapse except for the residual angular momentum which cannot be dissipated: a disk. Particles in collisionless systems cannot dissipate their energy by converting it to heat, nor cancel out their momenta with that of other particles to allow further collapse. Globular clusters became collisionless before complete gravitational collapse. Disk galaxies never became collisionless (they contain significant amounts of gas), and so formed disks.

Elliptical galaxies, disk galaxy bulges, and dark matter halos are also spheroidal because they are collisionless.

Answer 2

A globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is derived from the Latin globulus—a small sphere. A globular cluster is sometimes known more simply as a globular.

There are many shapes and classes of galaxies, but very generally and simply stated, globular clusters are a beginning stage in the formation of a galaxy, while the flat disc appearance in the later development is a product of the galaxies central black hole and the accretion process .

The fact that this is bugging you is the true definition of scientific inquiry. You can find much more detailed information by searching the web for "galaxy" and  read about formation.