“Amavi” perfectum est, “amabo” futurum.

They are both finite verb forms of amare (to love).

• amavi = first person singular, perfect active indicative
• amabo = first person singular, future active indicative

So both mean I ... something, with the ending itself showing the subject I.

Because they belong to different tenses.

• amavi is a perfect form, used for an action viewed as completed.
• amabo is a future form, used for an action that will happen later.

In beginner Latin, amavi is often translated as either I loved or I have loved, while amabo is I will love.

Because these are neuter forms.

Latin often understands an omitted noun such as tempus (tense), which is neuter:

• tempus perfectum = perfect tense
• tempus futurum = future tense

So perfectum and futurum are neuter because they agree with an understood neuter noun. They can also function by themselves as shorthand for the perfect and the future.

The second est is simply omitted because it is understood.

Latin often leaves out a repeated word when the meaning is obvious. So the full sense is:

• amavi perfectum est
• amabo futurum est

In English we do something similar sometimes, as in John is tall, Mary short.

Because Latin usually does not need a subject pronoun when the verb ending already shows the person and number.

• amavi already means I loved / I have loved
• amabo already means I will love

You can add ego if you want emphasis, contrast, or clarity, but normally it is unnecessary.

They are built from different stems.

For amavi:

• verb: amo, amare, amavi, amatum
• perfect stem: amav-
• ending: -i
• result: amavi

For amabo:

• present stem: ama-
• future marker for 1st and 2nd conjugation verbs: -bo
• result: amabo

So the two forms are not made in the same way, because Latin forms the perfect and future differently.

Not exactly.

Latin amavi covers more than one English possibility. Depending on context, it can mean:

• I loved
• I have loved

So Latin’s perfect tense combines uses that English often separates into simple past and present perfect. That is why English speakers often need time to get used to it.

Because the sentence is talking about the words themselves, not using them normally in a sentence.

In English, we do the same thing when we say things like:

• Run is a verb.
• Quickly is an adverb.

The punctuation marks are a modern editorial habit. Ancient Latin texts did not use quotation marks in this way.

In many teaching materials, yes, you would often see:

• amāvī
• amābō

Macrons show vowel length:

• ā is long in both forms
• ī is long in amāvī
• ō is long in amābō

They are helpful for pronunciation and sometimes for distinguishing forms, but many printed Latin texts leave them out.

In a standard restored classical pronunciation, approximately:

• amāvī = ah-MAH-wee
• amābō = ah-MAH-boh
• perfectum = per-FEK-tum
• futūrum = foo-TOO-rum

The stress falls on the second-to-last syllable if that syllable is heavy or long; otherwise it falls earlier. That is why amāvī, amābō, perfectum, and futūrum all have stress on the middle part.