Are there different kind of chanting styles depending on the type of temple you go to?
There are numerous, different kinds of chanting styles. And they aren't just restricted to temples, but can also be found on the yajna grounds. Chanting at most temples is usually of a very "general" type. In other words, this type of chanting is more casual. It isn't orthodox. For that, one would have to listen to the recitation of Brahmins that follow certain Vedic recensions (i.e., shakha-s). The following should relay this pluralistic reality. Keep in mind, the chanting that you are about to hear is of a very ancient method. The incantations are perfect. These are not of a casual nature, but of a very traditional and orthodox setting. Chanting such as the following can be easy to come across online, but is extremely difficult to hear in real life. This is because such orthodox communities tend to congregate together and follow the prescriptions of their tribal societies, to the exclusion of coming into contact with outsiders unless the Vedic rite of sponsorship is conducted.
For starters, the chanting you may come across in many temples is something like the following---of a casual nature, not specifically "Vedic":
[youtube]iGZouJ1sm8Q[/youtube]
The above is not really "Vedic", per say. Even though the mantra-s are to be found in the Veda-s, the incantation follows no prescribed method. This is what I refer to as "casual". As per tradition, such a "lazy" approach to incanting Vedic mantra-s is actually counterproductive. If one is to recite Vedic mantra-s, they have to be incanted properly. Otherwise, they are voided because of the rules of Sanskrit recitation.
In comparison to the above, the following is not casual. In fact, the following is very, very traditional. The incantation you are about to hear is so old, that it precedes the advent of numerous sampradaya-s. In fact, its incantational patterns go back to a time when sampradaya-s didn't even exist---try, say, 1200 B.C.E.:
[youtube]2wkEU1GYD6U[/youtube]
The above, as compared to the first video, shows hotr-s (reciters of the Shri Rgveda) of a specific shakha (i.e., recension) from the Nambudiri community of Brahmins.
The following is also Vedic, traditionally. But, in stark contrast to the recitation of the Nambudiri-s, the reciters of the following video are of a different recension, as well as different recensions altogether. And thus their recitation is different. The video shows hotr-s as well as udgatri-s, the later being those that sing the Saman-s of the Shri Samaveda:
[youtube]SgR9sdy6y8A[/youtube]
So as you can see, there are various styles of Vedic chanting. There is also Bhaktic chanting. I presume this is what you meant by "chanting". But this form of chanting doesn't really follow any traditional prescriptions. In fact, it's like singing casual, devotional songs. These are not Vedic. For example:
[youtube]L74zZnYvvyM[/youtube]
I hope that was at least somewhat helpful.