“Amans” participium est, et “amatus” quoque participium est.

They are both participles, which are verbal adjectives: forms that come from a verb but behave like adjectives.

• amans = the present active participle
• amatus = the perfect passive participle

Both come from the verb amo, amare.

The difference is mainly one of time and voice.

• amans is present and active: it describes someone doing the action of loving.
• amatus is perfect and passive: it describes someone or something that has been loved.

So they are both participles, but they do not mean the same thing grammatically.

Because Latin forms different participles in different ways.

• The present active participle is usually formed from the present stem with -ns in the nominative singular:
  ama-
  • -ns → amans
• The perfect passive participle is formed from the supine stem with -tus:
  amat-
  • -us → amatus

So the different endings show that these are two different participial forms.

They are really both, in a way.

They come from a verb, so they keep verbal meaning:

• amans still has the idea of loving
• amatus still has the idea of having been loved

But they decline like adjectives and can describe nouns:

• vir amans = a loving man / a man who loves
• puella amata = a loved girl / a girl who has been loved

That is why participles are often called verbal adjectives.

Here they are nominative singular.

That makes sense because each one is the subject of est:

• Amans participium est
• amatus quoque participium est

So in each clause, one participle is being identified as a participle.

In the nominative singular, amans can be masculine, feminine, or neuter, depending on the noun it goes with.

As a participle of the third declension, its nominative singular form is the same for all three genders:

• masculine: amans
• feminine: amans
• neuter: amans

Its other forms show the declension more clearly, such as amantis in the genitive singular.

Not in that exact form. amatus is specifically masculine nominative singular.

The other nominative singular forms are:

• masculine: amatus
• feminine: amata
• neuter: amatum

So unlike amans, the perfect passive participle changes form more obviously by gender in the nominative singular.

Because each clause talks about one word at a time:

• Amans participium est = amans is a participle.
• amatus quoque participium est = amatus is also a participle.

Each subject is singular, so participium is singular too. If Latin were saying both are participles in one statement, then a plural form would be more likely.

quoque means also or too.

In Latin, quoque often comes after the word it especially emphasizes. So:

• amatus quoque = amatus too / amatus also

That placement is very normal in Latin.

They come from amo, amare, meaning to love.

From that verb, Latin forms:

• amans = present active participle
• amatus = perfect passive participle

So both words belong to the same verb, but they represent different participial forms of it.

They can be used like adjectives modifying nouns.

Examples:

• vir amans = a loving man / a man who loves
• femina amans filios = a woman loving her children / a woman who loves her children
• puer amatus = a loved boy / a boy who has been loved
• urbs amata = a beloved city

So the sentence is not using amans and amatus in full context; it is simply identifying them as examples of participles.

It can do both, depending on context.

As a perfect passive participle, its basic force is:

• having been loved

But because participles often function adjectivally, it can also be translated more naturally as:

• loved
• beloved

So in actual reading, you often choose the English wording that sounds most natural while still matching the Latin grammar.