Temporary and Permanent Magnets
There are different forms of iron. We want to look at soft iron and steel. These have different magnetic properties.
Consider a soft iron rod and a steel rod. When you touch each one with a permanent magnet, the rod becomes magnetised.
Then remove the permanent magnet. The soft iron rod loses most of its magnetism. The steel rod keeps most of it.
When attracted by a permanent magnet, a soft iron rod becomes an induced magnet at first. The moment the permanent magnet is removed, the soft iron rod is not a magnet anymore.
On the other hand, if we use a steel rod, the steel rod will remain a magnet even after the permanent magnet is removed.