Type 1 has a problem in that the plunger (or slug) is not within the main magnetic field so the pull force is relatively low. The nearer the slug gets to the coil armature the greater the force experienced
They both have the problem that the magnetic circuit is not closed so all the forces will
be relatively small. Usually solenoids have a steel frame that completes the magnetic circuit
Type I has a large piece of iron in the coil, the fact the other piece isn't in a coil
isn't a problem since its close by and is attracted just as a piece of iron is to a permanent
Type 2 plunger is the armature and is contained within the magnetic field so the pull action is much higher. The plunger will attempt to "balance" itself to the centre of the magnetic field. Providing the plunger is longer than the coil you can get it to extend beyond the coil end.
The balance effect applies to a single iron rod in a coil and is a weak force - here there's
a lump of iron at the end of the winding, so again there is a magnetic attraction between
an electromagnet and a lump of iron (stronger force). Normally this more common type
has a frame completing the magnetic circuit so that their is only one gap and the forces
are a lot higher still.
Magnetic circuits are strongly limited by the gap or gaps as these have far higher
reluctance than the iron or steel (by factors of 1000 or so). Calculating detailed magnetic
forces in the presence of ferromagnetic materials is a rather involved bit of calculus,
alas... The forces on the coil are a lot less than the forces on the iron, since the bound
currents in the iron are many times larger than the free currents in the coil(*). The large
forces are always between two bits of iron/steel, never between the coil and something else.
(*) bound currents are due to electron spin in ferro/ferri-magnetic materials and
are quantum mechanical in nature. For a material with a permeability of 1000 the
bound currents can be upto 1000 times the free currents in a coil around it.
For instance neodymium iron boron magnets have bound current density of
about ~500kA/m, which is close to the maximum achievable in any ferromagnetic