This refers to the fact that, in Yu-Gi-Oh, monster "archetypes" are based in the card names. In the original Japanese cards, the name usually contains a certain phrase that identifies a monster as part of an archetype. However, in English and other languages, this sometimes gets lost in translation. The most common cause of this is that, at the time of translation, the name was not a planned archetype. To correct this, a wording convention was eventually created called an Archetype Condition, which states that any effect looking for an "'X' card" may also point to this card. Eventually, this also carried over back to the Japanese cards as well if the original card would not be named to match an intended archetype.
Examples of when this became an issue can be seen in the HERO archetype (where, as new HERO types were created, existing cards that were intended to work with all HERO archetypes had to be continuously reworded until it was decided to retroactively rename the English cards. See the history of Elemental HERO Stratos for examples of that) and the Daemon archetype (where, for many years, the TCG simply had to maintain a "List of Archfiend cards", as many older cards did not translate Daemon consistently until Archfiend became an archetype and the older cards needed to become Archfiends as well).
In the case of Dragon Spirit of White, the intention was for this to be considered a "Blue-Eyes" card like Blue-Eyes White Dragon. This allows it to be used as a Blue-Eyes card when an effect calls for Blue-Eyes cards generically. Specific examples include:
- Blue-Eyes Spirit Dragon - a Synchro monster whose materials are "1 Tuner + 1 or more non-Tuner "Blue-Eyes" monsters"
- Deep-Eyes White Dragon - an Effect monster whose effect triggers "When a face-up "Blue-Eyes" monster(s) you control is destroyed".
- Beacon of White - a Spell card whose activation condition requires a certain number of "Blue-Eyes" monsters in your graveyard.
However, this does not make this card a "Blue-Eyes White Dragon." Archetype conditions only make the card a generic instance of the archetype they refer to. They cannot be used to replace cases where full, explicit card names are necessary. As a result, Dragon Spirit of White cannot be used as a Fusion Material for Blue-Eyes Twin Burst Dragon because it explicitly lists "Blue-Eyes White Dragon", not "1 "Blue-Eyes" Monster". For that, you would need a card that specifically says that the monster's name "becomes" another card's name.
An example of that can be found in Blue-Eyes Alternative White Dragon, whose effect, in part, reads
"This card's name becomes "Blue-Eyes White Dragon" while it is on the
field or in the Graveyard."