A catheter is a tube that is inserted into the body or a body cavity/orrifice. Such as: a suction catheter for NT or tracheal suctioning, a central venous catheter for administration of IV medicaitons and fluid, Swanz-Ganz catheter for measuring cardiac output and fluid status, just to name a few.
In casual conversation when a nurse reports "he has a catheter" most likely they are talking about the urinary kind. We even say "he has a foley", meaning the same thing.
Straight cathing is a urinary catheter tube inserted into the urethral opening into the bladder to empty it of urine once, then you take it straight out. You do not have a balloon on this and it doesn't stay in place. This is usually done when the pt doesn't need a catheter but needs the bladder emptied immediately. Some people whith spinal injuries and diseases straight cath themselves several times a day since they cannot empty on their own.
Sometimes this is done prior to surgery to prevent a full bladder from getting in the way of the operative site(or nicking the bladder)