There are many types of animal. You can divide the animals into different subgroups: Mammals, Birds, Insects etc. Or you can divide them by what they eat (Carnivore, herbivore, insectivore etc). Or what eats them (prey or predator) Or by their usefulness to humans (domestic, pet, farm, wild, pest etc)
Some categories overlap, some are fuzzy, some are scientific, some are not very useful. Sometimes a particular animal can be a predator in one situation, but prey in another.
It is the same with nouns. You can categorise them in different ways, by meaning such as "abstract" or "Concrete". Or by grammar "count" and "non-count". Or by their position in a sentence "subject" or "object". Some of these categories overlap, sometimes a word can be countable in one situation but uncountable in another.
To clarify: Gerund/participles are not nouns, but a form of a verb. Gerund/participals are not nouns, but they are like nouns in some ways (for example they can be the subject in some sentences)
A noun phrase is a phrase that is headed by a noun. It will often have other words such as determinatives (like "the"), adjectives, and even sub-phrases such as a relative clause. A compound noun is a short phrase or long word made of two (or more) nouns.
Example
The local playgroup is having a cake sale.
"Playgroup", "cake" and "sale" are nouns.
"Playgroup" and "cake sale" are compound nouns. The latter is an open compound.
"The local playgroup" and "a cake sale" are noun phrases ("local" is an adjective)
"having" is a gerund/participle (a type of verb)
"The local playgroup" is the subject of the sentence.
"a cake sale" is the object of the gerund "having"
The gerund phrase "having a cake sale" is the complement of the verb "is".
"sale" and "playgroup" are both countable. "cake" is uncountable (but in this sentence the only one that matters is "sale" because it is "a" sale)
"concrete" and "abstract" are not very useful categories, because they are very fuzzy. I'd say all the nouns here are concrete.
To echo the comment below. Words don't get put into categories until they are used in language. You can't ask "What type of word is 'park'?". You can ask "What type of word is 'park' in the expression 'I went to a park'?"