When you talk about participles in English, there are two. The traditional names for these forms are "present participle" and "past participle"
Unfortunately, those names are misleading and confusing. The so-called present participle has nothing to do with the present tense but everything to do with the continuous aspect. Likewise, the so-called past participle has nothing to do with the past tense but everything to do with the perfect aspect. Even "perfect aspect" is a misleading, confusing name, as it has nothing to do with the completeness of the verb's action but everything to do with the results of the verb's action.*
Here's a revised list:
1) Traditional name: present participle. Purpose: marks the continuous aspect (or progressive aspect, especially if the verb's meaning involves change). Form: -ing. Examples: being, going, breaking, sleeping, changing, ringing
2) Traditional name: past participle. Purpose: marks the perfect aspect. Form: -en, -t, -ed, and others; or, a changed vowel. Examples: been, gone, broken, slept, changed, rung
The variety of past participle forms is simply an accident of history. Your best option is to learn each verb's forms separately. This is why the past participle is one of the principle parts of verbs.
As you already know, the participles of "to go" are "going" and "gone". In the sentence "I went shopping", "went" is not a participle at all. "Went" is simply the past-tense form. However, "shopping" is what we call a present particle form.
As should be obvious, the phrase "went shopping" can't represent a verb form. There are two words in the verb.** There are two forms. On the other hand, the two forms combine into one construction -- a verb in the active voice, past tense, continuous aspect and indicative mode, often called the "past continuous" for short.
There are quite a few verb constructions in English, many of which include participles. For instance, "I was hoping to be gone shopping by now" contains a predicate with a past-tense finite verb, a continuous participle, an infinitive, a past participle, and finally a continuous participle.
* We can see this clearly in a sentence like "I have eaten a lot, but I have not finished eating." Such a sentence would be senseless if the perfect "eaten" truly meant that the action were complete.
** or two verbs in the phrase. The name "verb" is quite confusing on its own. It would be helpful to have an easy, clear way to distinguish between verb-as-a-part-of-speech and verb-as-a-part-of-the-sentence.