This catch is known as the Lamb's Tail Tube catch.  Without the strip of metal and the ball of solder it is just a tube catch.

This is known as a T-pin and you can see why.  It resembles a capital T. Widths vary but 1/2 inch wide is common.

This is also a T-pin however it is much more narrow. Commonly called the N-type or Narrow T-pin. 

Spring Pin with cover plate. Badge makers often stamped their hallmark into the cover plate.

A common pin catch that resembles the letter C is aptly called the C catch.

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