Is there a difference between a Solemn Mass and "regular, everyday" Mass?
Its a high Mass, so most parts of the Mass are sung/chanted and incense is burnt. As you probably know now the difference is that at regular mass not everything is sung i.e. The Our Father, The Sanctus etc.. and the fact that incense is not burnt at regular Mass, at least not in our Parish.
edit- I actually preferred the Solemn Mass, very beautiful.
I think you are getting a bit mixed up here. There are two forms of the roman rite;
The Ordinary Form:
This is the Form of Worship that we see most commonly in the Church. This Form was created in 1969 after the reforms of the Second Vatican Council. In this form, there is no distinction between Solemn Mass, Low Mass etc. There is simply Mass with a Deacon, Mass with con-celebrants etc. It is very simple and basic and personally, I think is very loose in it's rules.
The Extraordinary Form:
This Form has technically existed since about 400AD (some prayers were used during the time of St. Augustine. It was compiled and united together in 1570 by Pope Pius V (I think this is correct). It has had many very small revisions since then. It is commonly known as the "Tridentine Mass", is always and only said in Latin nowadays and it has different forms of celebration;
- Low Mass; Very simple Mass, with no Music. Said completely by the Priest and servers. It is solemn, full of gestures and very majestic, and very strict, it is very beautiful to witness
- Missa Cantata; "Sung Mass" with Incense - the whole Mass, except for the Consecration, which is always carried out in total silence in the Tridentine Mass, is sung by the Priest and Choir, with some exceptions (the readings and homily etc.)
- High Mass; Same as the Missa Cantata but assisted by a Deacon, Subdeacon and sometimes an Assistance Priest. Of greater solemnity. This would be referred to as a "Solemn Mass" - this may answer your question
- Pontifical High Mass; The Same as a High Mass, but celebrated with a bishop with more solemnity and more gestures, mainly proper to the Bishop.
I think I have answered your question. The Ordinary Form can be celebrated with solemnity, but not to the standard that the Solemn High Mass in the Extraordinary Form has. For more info, check here: en.wikipedia.org/wiki/Tridentine_Mass
In magnam fidem,
Also, here are some videos that may help:
1) A Low Mass celebrated by an FSSP Priest. It has commentary throughout about the meaning of the Mass: youtube.com/watch?feature=player_detailpage&v=3eb0R-edS3Y
2) Missa Cantata celebrated by an SSPX Priest in Paris. Very good music here, you may wish to observe the ornate use of Gregorian Chant. FYI, the SSPX are not in Communion with Rome at the moment, they are a breakaway society for the time being, but the Pontifical commision "Ecclesia Dei" has affirmed that their Masses are still valid so. Here is the video: youtube.com/watch?feature=player_detailpage&v=c32brXXx5k8
3) High Mass - not very different to the Missa Cantata. I believe this was celebrated in England. Here: youtube.com/watch?v=i7qdxX5rkYI
4) Pontifical High Mass: Here is an Pontifical High Mass in the Extraordinary Form with the Ordination of Priests to the FSSP. Here: youtube.com/watch?feature=player_detailpage&v=LRORqBf1lIg
Hope I've helped!