I have found a preliminary answer to a question that has been bothering me for some time. The issue is this: if everything in creation, including the manifestation of God, proceeds from God by way of emanation, what do Baha'is mean by the term 'manifestation' in the phrase 'manifestation of God'?
Unfortunately, I cannot find in the writings a definition of the word 'emanation'. It is always explained using analogies. A common analogy Abdu'l-Baha gives for proceeding from emanation is the rays of light from the sun. It is said that these emanate from the sun because the sun does not resolve itself into the rays; rather, the rays just come out of the sun, while the sun remains unchanged. Other analogies are action from an actor, writing from a writer, a discourse from a speaker. These are all examples of proceeding through emanation because the essence or reality of the cause does not literally appear in the effect. In other words, the cause does not divide into parts in order to create the effect. Rather, the effect just comes out of the cause.
Proceeding through emanation is always contrasted with proceeding through manifestation. Abdu'l-Baha does define proceeding through manifestation (SAQ ch54): "the proceeding through manifestation means the manifestation of the reality of a thing in other forms". A common example he gives is that of a seed. A seed proceeds through a process of manifestation to become a tree. This is because the actual seed - its reality or essence - changes form, taking on the form of a seedling, and so on until it is a fully grown tree. Given this idea, I think all forms of 'seeds' would proceed through manifestation. For example, the egg and sperm, once joined, would proceed through manifestation to become an adult human. But other, different, examples include the way that water changes its form into steam or ice, and the way the ocean changes its form continually with the activity of waves.
The reason the contrast between proceeding through emanation and through manifestation is emphasised in the writings is because some philosophers believed that creation was a manifestation of God; in other words, something of the essence of God was to be found in all things. But the Baha'i writings reject this outright, emphasising the important distinction between proceeding through emanation and through manifestation. All things emanate from God - that is, come out of God - but they are not manifestations of God - that is, the essence of God does not change form and become a part of created things. This would mean that God had become divided into parts. Instead, Abdu'l-Baha explains (ch54) that God is in one condition and that condition never changes.
This brought me to my question: if every created thing is an emanation of God, what do we mean by the word 'manifestation' when we refer to Baha'u'llah as the 'manifestation of God'? For, it is certain that the manifestation of God is an emanation of God and not a manifestation of God in the sense that we discussed above. The answer came in SAQ ch54 where Abdu'l-Baha is explaining proceeding through manifestation. He says:
"But the proceeding through manifestation (if by this is meant the divine appearance, and not division into parts), we have said, is the proceeding and the appearance of the Holy Spirit and the Word, which is from God." (p 206)
I finally woke up to the very important distinction that is made in the brackets. The bit in brackets makes it clear that there are two meanings to proceeding through manifestation:
1. the manifestation of the reality of a thing in other forms - this is the seed becoming a tree, which involves the seed dividing itself into parts
2. the divine appearance.
So the appearance of the divine in creation - or, put another way, the manifestation of the divine in creation - is a different sense of the word 'manifestation' to that of the reality of a thing resolving itself into different parts and forms. It seems to me that the first definition is a philosophical one - it is a special technical meaning used by philosophers. The second definition is more in line with the dictionary definition: "the demonstration, revelation, or display of the existence, presence, qualities, or nature of some person or thing". (New Shorter Oxford English Dictionary)
Abdu'l-Baha then goes on to explain what is meant by proceeding through manifestation in the second sense - the divine appearance. Basically, the proceeding through manifestation in this sense means the appearance of the Holy Spirit and the Word, which are the perfections of God. This is very close to the dictionary definition of 'manifestation', the idea of the display of the qualities of a thing. Abdu'l-Baha gives an example of this: the reflection of the sun in a mirror. This reflection displays all the qualities of the sun - the heat, light, and image. So when we say that Baha'u'llah is a 'manifestation of God', we mean that he manifests or displays the perfections and qualities of God, including God's existence, presence and nature. This is in line with the dictionary definition of 'manifestation' but not the philosophical one.
But note that the reflection of an image in a mirror is still an emanation - the image emanates from its cause and appears in the mirror. The image is a manifestation in the sense of a display of its cause, but an emanation in relation to how it originates from its cause.