Hello, I hope this helps. A tertia is another name for a division, while a brigade is a brigade, which is a larger regiment. Today a division is commanded by a Major General and has anywhere from 10,000 to 15,000+ soldiers, while a brigade is commanded by a Lieutenant Colonel or Colonel but today it's a Brigadier General. If you look at the 1st (United Kingdom) Division, its houses 8 brigades. In the English Civil War terms, the New Cornish Tertia Army was 4 Royalist infantry regiments and held most of England and Wales during the war. Some secondary sources use tertia and brigades for the same meaning. The New Cornish Tertia Army had around 5000-6000 men and 1000 horses, while an infantry regiment would have 10-12 companies of 100 men, and maybe be formed in a brigade with 2 other regiments to form a 3000 man force. A brigade would just be one type of soldier such as infantry or cavalry.
Here is a link that goes into more depth about different soldier types during the English Civil War.