grammar - What is the difference between ふくむ and ふくめる

The Progressive-Japanese English Dictionary suggests 含める is the same as one meaning of 含む but it is not explained. Is this correct? I have two theories:

1. 含める= 含む when the latter means include/contain

This is based on the following examples

鉄分を含んだ水｜water containing iron

その団体には女性2人が含まれている｜The group includes two women.

And:

子供を含めて300人だ｜There are 300 people, including the children.

郵送料を含めて5,000円だった｜It cost 5,000 yen, postage included.

Which leads me to think:

水が鉄分を含む　＝　水が鉄分を含める　（Water contains iron)

However we don't seem to find the following use: 鉄分を含める水

This leads me to (2):

2. 含める is used when the action of one party actively includes an object within in a group (which is grammatically an indirect object)

As in the following example:

彼らの名をリストに含めた｜We included their names on the list.

Even in the following cases an indirect object seems to be implied

郵送料を含めて5,000円だった｜It cost 5,000 yen, postage included.

私は税金を含めて月40万円の収入がある｜I have an income of 400,000 yen a month before taxes.

Because they could easily be rewritten:

If I include postage, it cost 5000 yen.

If I include tax, my monthly income is 400,000 yen.

or,

Could we also write the following?:

郵送料を含んだ5,000円だった

私は税金を含んだ月40万円の収入がある

If so then these two verbs are interchangeable when the sense of include/contain is taken

Please let me know if my question is not clear.

Answer

I might not have thought of all situations, but I don't find the two verbs generally interchangeable.

含む means "contain" or "include", i.e.

水が鉄分を含む the water contains iron 料金は消費税を含む the price includes consumption tax

the subject 含める is an animate agent who includes something into something else, i.e.

私は名前をリストに含める I include the name in the list

Although the same verb is used for "A includes B in C" and "B includes C" in English, the two usages are different, if you really think about it.

If 含める is synonymous with anything, I'd say it's 含ませる, the causative of 含む.

Comments on your examples: Although understandable, I don't find "水が鉄分を含める" grammatical. As for "郵送料を含んだ5,000円だった", are you using the past tense instead of "含んで" for some reason, or is it a typo?