In terms of interpretation, 听见 and 听到 are practically the same.
However, they are different in terms of structure: 听见 is a combination of a verb (听) with a lexical element (见), both of which have compatible semantic fields. There are not many combinations of "verb + 见" (看见，遇见 or 碰见) as the semantic field of 见 is restrictive.
On the other hand, 听到 is a combination of a verb (听) with a grammatical element (到), which behaves very much like an aspect marker like 了，过 and 着. As a grammatical element, 到 does not have a concrete lexical meaning. It can be used with many verbs, and its interpretation is a function of the property of the verb and the sentence context. For example:
我昨天在商场看到李老师。
他收到一个莫名其妙的包裹。
那个小孩捡到十块钱，交给了警察。
他吃饭太匆忙，咬到舌头。
小心，不要割到手。
In these examples, the process is interpreted as "non-intentional" or "accidental".
When the context involves a planned action with an objective, the combination of "verb + 到" will give an interpretation of "manage to do" or "succeed in doing". For example:
他去了领事馆三次，终于拿到签证了。
这场音乐会很多人想看，我们会买到票吗？
你找到你的钱包了吗？