Yes, the word order makes a slight difference in modality which describes the thought/emotion/belief of the speaker about the contents of a sentence/sentences towards the listener.
- 私は辞書{じしょ}を買い{かい}ました。
- 辞書{じしょ}を私は買い{かい}ました。
Both are completely accurate as a sentence in Japanese and mean 'I bought a dictionary' in English as you said. These two sentences can be decided into 3 clause phrases called 文節{ぶんせつ} in Japanese. 文節 is composed with an independent word (i.e., noun, adjective, verb) and an adjunct word (i.e. は, が, を).
1'. 私は / 辞書{じしょ}を / 買い{かい}ました。
2'. 辞書{じしょ}を / 私は / 買い{かい}ました。
Japanese tends to place the phrases in order of what the speaker wants to impress. In the sentence #2', 辞書{じしょ}を is placed in the first of the sentence, so the speaker wants to impress 辞書{じしょ}. Although, は is following 私 in the sentence. は is a topic marker and [noun/noun clause + は] is apt to position in the first in the sentence because it tells what is the topic/theme. So the sentence #2 & 2' sound a bit unnatural/unreal for some people. To make it sound more natural, you can replace を following 辞書{じしょ} to は and は following 私 to が*;
辞書{じしょ}は私が買い{かい}ました。
As for/talking about what I bought, it is a dictionary.
が is the subject marker in this sentence to tell who is the doer of the action (買いました). This will be another discussion, so I won't go further than this now.