The Concise Oxford English Dictionary (6th ed.) defines a thief as "a person who steals another person's property, especially by stealth and without using force or threat of violence"; to rob as to "take property unlawfully from (a person or place) by force or threat of force"; and a bandit as "a violent outlaw or outlaw belonging to a gang".
It seems that there might be a similar distinction in Greek between λῃστής - the word used in Matthew 27:38 - and κλέπτης. We have, for example, in the RSV translation of the Gospel according to John:
Truly, truly, I say to you, he who does not enter the sheepfold by the door but climbs in by another way, that man is a thief [κλέπτης]
and a robber [λῃστής] (10:1).
Also, in the Septuagint:
If thieves [κλέπται] come upon you or robbers [λῃσταὶ] by night, then to what place will you escape (Obadiah 5, Orthodox Study
But the distinction is ambiguous. While λῃστής is clearly used to convey the COED sense of "robber", as in
A man was going down from Jerusalem to Jericho, and he fell among robbers, who stripped him and beat him, and departed, leaving him half
dead (Luke 10:30, RSV)
and κλέπται seems that it might convey the COED sense of "thief", as in
If the householder had known at what hour the thief was coming, he would not have left his house to be broken into (Luke 12:39, RSV)
neither seem to carry these meanings exclusively. We have, for example,
The thief [κλέπτης] comes only to steal and kill and destroy (John
where κλέπτης reflects violence, and also
It is written, ‘My house shall be a house of prayer’; but you have made it a den of robbers [λῃστῶν] (Luke 19:46, RSV).
With the above exceptions, however, it does seem that λῃστής - which appears 15 times in the New Testament and 9 times in the Septuagint - generally conveys the COED sense of "robber", whereas κλέπτης - which appears 16 times in the New Testament and 17 times in the Septuagint - generally conveys the COED sense of "thief".
Note that there is an additional confusion here, in that the antiquated meaning of "thief" is probably different than the modern. The King James Version often uses the word "thief" where the word "robber" might have been more suitable in modern usage. Luke 10:30 reads, for example:
A certain man went down from Jerusalem to Jericho, and fell among thieves, which stripped him of his raiment, and wounded him, and
departed, leaving him half dead.
Modern versions like the RSV and ESV seem to try to preserve the distinction between κλέπτης and λῃστής, and translate each as "thief" and "robber", respectively. The NKJV seems to be somewhat loose, often preserving the KJV "thief" for λῃστής. The NRSV seems to have taken some license in assuming that the two "robbers" worked together in a band (and hence were "band-its").