There are various ways to analyze passives in Japanese grammatically (see Ishizuka, p. 174), but I will be presenting a specific view which I really like, which is Ishizuka's.
When you passivize a sentence in Japanese (by adding -(r)are- to the verb), you
- lift a non-が argument of the active sentence to が, and
- lift the が argument of the active sentence to に.
The non-が argument can be anything -- sometimes it's the を argument, sometimes the に argument, sometimes the から argument, or sometimes even a possessive の lower down in the structure, etc.
(Note: There is also another type of passive where there is truly a new argument added, not pulled out from the original active sentence -- but not all native speakers accept them and they aren't needed to discuss this question. See Ishizuka, p. 263.)
So, I would say these are the original active sentences of your passives:
泥棒が （私から） 財布を 盗んだ。
⇒ （私が） 泥棒に 財布を 盗まれた。
Namely, 私から gets promoted to 私が, and 泥棒が gets promoted to 泥棒に.
(Note: The 私の version is probably just as fine an original sentence for this.)
泥棒が 財布を 盗んだ。
⇒ 財布が 泥棒に 盗まれた。
Here, 財布を gets promoted to 財布が, and 泥棒が gets promoted to 泥棒に.
So, while that is a little syntax which you may or may not believe, is there an actual semantic difference between the two constructions?
In general, there is a difference in adversarialness, though in this specific case not really.
The usual difference is that there is a connotation of the が-marked argument in the passive sentence being "affected" (which usually gets further interpreted as adversarial due to information structure) when it was originally marked by:
- "on" に (e.g., 雨が太郎に降った。⇒太郎が雨に降られた。)
- の (e.g., 直美がケンの子どもを叱った。⇒ケンが直美に子どもを叱られた。）
- から (e.g., 妻が夫から逃げた。⇒夫が妻に逃げられた。）
while the others (other にs, を, etc.) do not result in the が-marked argument being "affected".
However, both of your sentences are adversarial, simply because getting your wallet stolen always affects you negatively.
In English, consider
John saw Mary entering the building at 6 o'clock.
Mary was seen entering the building at 6 o'clock by John.
Mary is clearly more negatively affected in the latter.
A thief stole John's wallet.
John had his wallet stolen by a thief.
John was negatively affected in both just due to "thief" and "stolen".
So while 泥棒に財布を盗まれた。 forces the adversarialness, I think 泥棒に財布が盗まれた。 and 泥棒が財布を盗んだ。 are equally as adversarial anyways simply due to the words used.
Person being stolen from
As yu_ominae points out...
泥棒に財布を盗まれた。 requires an explicit understanding of someone being stolen from / there being a wallet owner. If you look at the syntax, this is because the thing in the が-position (which is omitted, but only due to context making it clear) is who it is being stolen from or the owner of the wallet.
On the other hand, 泥棒に財布が盗まれた does not require that understanding, because it is really just like the passive in English ("The wallet was stolen by a thief"), where, while who it is being stolen from could optionally be added as an adjunct (私から/"from me"), it is not a part of the actual sentence.
Ishizuka, T. (2010). Toward a Unified Analysis of Passive in Japanese: A Cartographic Minimalist Approach.
Relevant sections are:
- Raising things to が: pp. 67-150.
- Adversarial connotations: pp. 245-261.
But the entire thing is quite nice.