The major difference between "pro" and "consumer" equipment is generally their suitability for their purpose. A home theater setup needs to sound pleasing to the ear without much manual work, only fill up one room with sound, and play from generally a single source. It also (usually) needs to be affordable enough that people will by them. A huge live-sound rig, however, might have to fill up an arena without distorting, mix together lots of sound sources with varying properties, and be adjustable by a human operator to fit the situation. They generally cost more since they're more like business investments for work purposes than consumer purchases for entertainment
However, I think the core of your question is really whether consumer and pro equipment are compatible. As in, could you use them together. At a basic level, they are - both of them generally deal with analog audio signals running over cables, however there are a variety of standards for voltage that are important to understand. In general getting this right is called impedance matching. You don't want to send a quiet signal into something expecting a semi-loud one, and you definitely don't want to send a too-loud signal into a system expecting something quieter. At best the signal will clip, and at worst it could damage the hardware.
Electric guitar into hi-fi stereo
An electric guitar signal is very faint ("instrument level"), much quieter than what a hi-fi system would be expecting ("line level", if I remember right), and so it's reasonable to assume that it wouldn't sound very good, if you could hear it at all. However, you could use a guitar amplifier with a line-level output jack, and that would probably work very well so long as you don't turn it up too loud and distort the signal through clipping.
In the case of an electric guitar, it's also worth noting that the amplifier is a very large part of the sound, and skipping the amp generally makes a guitar sound thin and undesirable.
iPod into a guitar amp
In general, there are two problems with doing this: the iPod is outputting a headphone-level signal, and might be too loud for the amp, causing distortion and possibly damage if your amp isn't rated to deal with those levels. Secondly, most guitar amps don't just make things louder, they also change the sound significantly, usually with creative use of distortion.
Many guitar amps, particularly combo-style practice amps, have separate line-level inputs which will accept an iPod or CD player just fine, as they are generally amplified separately from the guitar to avoid distortion.
So yes, these sorts of things can be combined, but you have to make sure the signals are appropriate. There's more to it than just cabling.