The definitions of the two kinds of material is the following:
A paramagnetic material (in short paramagnet) is not magnetized when there is no external field. However, when put in an external field it magnetizes parallel to the magnetic field (and is thereby attracted to both poles of the magnet). Once we remove the external magnet, the magnetization vanishes.
A ferromagnetic material (in short ferromagnet) is spontaneously magnetized, that is, without any externally applied field there is a magnetization of the material (which creates a field also in the space around the material). However, the interaction of a real world ferromagnet with an external magnet is a bit more complicated than your teacher summarized. I'll try to explain this in the following.
A normal slab of iron that was just cooled down from above the Curie temperature (that is the transition temperature from paramagnetism to ferromagnetism), or demagnetized in a high frequency magnetic field, does not create an external magnetic field.
The reason for this is that there are magnetic domains (sometimes called Weiss domains) in the material. Those are magnetized spontaneously along some direction, but the magnetization direction of the domains is not aligned, so the total field outside of the material (almost) cancels out.
Defects in the material (e.g. grain boundaries, impurities, etc.) lead to a certain pinning of the magnetization direction of these domains. Depending on the material (and the number of defects in it), it takes more or less energy to overcome this pinning. We say a ferromagnet is hard or soft depending on this.
A soft ferromagnet (e.g. soft iron used in transformer cores) will be attracted to both poles of a magnet, because the field strength of the magnet is strong enough to orient all the magnetic domains in the same direction. When the magnet is removed the individual domains undergo reordering due to thermal fluctuations and the remaining magnetization without an external magnet (the so called remanence) is typically weak.
A hard ferromagnet, on the other hand, (e.g. the rare earth ceramics used in neodymium magnets) has magnetic domains that are strongly pinned. So even when using a rather strong external magnet, they will not reorient. So, when oriented in a certain way, it will only be attracted to one pole of another magnet, but repelled by the other one.
There are materials that are intermediate in this scale, e.g. the kind of iron alloys used for nails. When you stick a nail directly to a magnet, they stay there. But you can stroke along them a few times with one pole of a moderately strong magnet, and this will create some remaining magnetization with a preferred orientation. When you create two such nails, they will act like small bar magnets, and each will have a north and south pole, such that the like poles repel, while the opposite poles attract.
Finally, the strength with which the material magnetizes (the so called susceptibility $\chi$) which says how strong the magnetic field in the material is compared to the external field, is much larger for ferromagnets than for almost all paramagnets. So a soft ferromagnet's attraction to a magnet will be much stronger than a soft paramagnet's one.
(There are, by the way, many other kinds of magnetic behaviour for materials: diamagnets magnetize anti-parallel to the field, so they are repelled by both poles of a magnet; antiferromagnets behave like strong paramagnets macroscopically, but they have anti-aligned elementary magnetic moments which align in a preferred direction, and the susceptibility gets much weaker above the transition temperature to paramagnetism; ferrimagnets are like antiferromagnets but the anti-aligned magnetic moments do not have the same strength, so a net magnetization remains).
