No, they are not all the same.
There are two basic styles, and even within the styles there are many that are similar but don't quite match up.
One style is the jack that fastens to the side of the trailer rail and swivels up. I really like these jacks because when you hitch up you just raise them up enough to get the load off, pull a spring loaded pin and rotate the mechanism 90 degrees and get it completely out of harms way. Fast, easy. These units either clamp to the side rails via large U-bolts or there may be a matching mount welded to the trailer. The clamp on ones are easy to replace or retrofit to an older trailer. If you have the welded on mount then you need to find a new one that has matching bolt pattern.
The other style of jack is normally mounted up in the peak of the "V" of the tongue. It could have been welded to the trailer or bolted down. If yours was bolted on, and you can find one with a matching bolt pattern, it is an easy replacement. I had to replace one not long ago and had to attach the trailer with a cutting torch to get the new one to fit.
It sounds like you have the swivel type that I described first, which is a lot easier to deal with. Just make sure that the new jack is rated for your trailer weight.
Rod