Lexicography
"Na'budu ": We Worship
"Abada": To serve, worship, adore, venerate, obey.
"Abbada": To enslave, subjugate, to make (a road) possible for traffic, to make serviceable, enthral,
"Abdun": A slave, bondman.
A servant.

When this word is used in the Quran in relation to Allah, it applies on those who willingly submit themselves to Allah and obey His Commands. For comparison
(Vocabulary of the Holy Quran, Dr Abdullah Abbas Nadvi).
Abdun is used in following senses:
Slave:
Bondsman by creation (Made by Allah):

"There is none in the heavens and the earth, but comes to the Most Gracious (Allah) as a slave"

The position of the Abdun (Slave) attained due to worship obedience: It is of two kinds:
(a). Those who are the devoted pure slaves of Allah:

"And remember our slave Ayuub"

"Verily, he (Noah) was a grateful slave"

"Blessed is He (Allah) Who sent down the Criterion to His slave (Muhammad), that he may be a warner to the worlds."

"As for My slaves - you have no authority over them "

"Eden Paradise- which The Most Gracious (Allah) has promised to His slaves, in the Unseen: Verily His Promise must come to pass"

"And the slaves of The Most Gracious (Allah) are those,
who walk on the earth, in humility and sedateness , and when the foolish address them,
they reply back with mild words of gentleness.":

(b) Those who pray out of the greed of the world:
The Prophet (Peace be upon him ) has condemned such people in the words: "Abdud-Dirham" and "Abdud-Diinaar" (Slave of money or wealth).

Such a person (worshiper) is called Aabidun as against Abdun which is more comprehensive and pure. The plural of Abdun in the sense of the pure slave is Abiidun and that of Abdun in the sense of Aabidun is Ibaadun.
(Mufridatul Quran, Imam Raghib Isfahani).

Ta-Abbada: To apply, To devote oneself . (J.G.Hava)
"Abada": To believe that Allah is the Only One Alone
To be base, low . (Misbaahullughaat, Abdul Hafeez)
"Abada": To subject
"Ta-Abbudu": Self consecration to God and His service . (Wortabet)
"Al-Abuudiyah": To show lowliness, humbleness, and humility before somebody.
"Al-Ibaadah": To show utmost lowliness, humbleness and humility .
Characteristics Of Aabidiin:
Submission as Slave People (Aabiduun):
Therefore in worship of Allah , the word "Al-Ibaadah" is more comprehensive.
"Have they not observed things that Allah has created:
how their shadows incline to the right and to the left,
making prostration unto Allah, and they are lowly"

"And to Allah prostrate all that is in the heavens and all that is in the earth, of the moving creatures and the angels, and they are not proud."
(Mufridatul Quran, Imam Raghib Isfahani)