Monograms and initials may seem interchangeable, and ciphers might seem like a wholly unrelated field, but they actually began much closer together. All three are ways of putting letters onto things, either decorative or as a mark of ownership, and anyone can use any (or all!) of them at will.
Initials are the simplest way of marking - each letter stands on its own. Whether you do one, two, three or even more, each letter is separate and distinct. Easy peasy. Most of the work we do here are initials; they're the easiest to design and pretty straightforward. Technically, this is just one initial and not a monogram, no matter how decorative:
Initials, unlike ciphers or monograms, are always made the way you read them. No flipping letters upside down to make them fit together, here. Everything is readable and minimally distorted.
Ciphers are a step more involved than simple initials; in a cipher, the initials are connected into a more cohesive whole (often with interlacing or overlapping). Each initial, taken apart, can stand on its own, without missing any parts. If the letters can be taken out of a design and be recognizable (though perhaps distorted) they're a cipher. The E and L might be weirdly slanted, but they are an E and an L, anyways.
Folks often think of a decorative initial as a monogram - after all, it says 'mono' for one and 'gram' for something written, right? A monogram, traditionally, is a set of letters combined into such a form that individual letters can't really be isolated. A better translation than 'one letter' would be 'written as one'. You can't pull apart the individual letters without things starting to get a bit wonky.
You might be familiar with this one:
If you take the J or T out of the monogram, the R's lose their center line. Monograms like this are hard to design for an entire alphabet; they're usually made specially for each person. They can be nearly as simple as initials:
or a bit mind-boggling:
Letters may be flipped upside down or mirrored at will in ciphers and monograms- the distinctive appearance of a monogram was sign enough, without necessarily being able to 'read' it.
Whether you prefer the readability of initials or the complexity of a traditional cipher or monogram, there's a million ways to make your mark. (But most everybody just calls them all monograms).