I need some information on community certificate ? I have some doubts

Full form of OBC is Other Backward Class and BC is Backward Class. In broad sense , OBC and BC are same . Both OBC and BC includes all the classes which are economically and educationally backward.

Backward classes include people/community who belongs to economically and educationally backward classes as classified by the State Government.
Other Backward classes include people/community who belongs to economically and educationally backward classes as classified by the Central Government of India.

Both categories have almost same privileges', facilities etc in the society. and BC category get more reservation than OBC category. Actually Other Backward Castes (OBC) category is considered as higher than Backward category in all respects.
Both the categories receive reservation from govt in jobs, education etc.

Coming to your next query : Thuluva Vellalar is included in both BC category as per the list available at http://www.bcmbcmw.tn.gov.in/bclist.htm
and in OBC also available at http://www.bcmbcmw.tn.gov.in/obc/faq/tamilnadu.pdf.

Backward class is a collective term used by the Government of India. The castes which are economically and socially disadvantaged and face, or may have faced discrimination on account of birth are termed as Backward classes. Many of the families in these castes were not having any own land. All these people are dependent on Forward Castes for employment. These are basically Schedule castes and scheduled tribes. There are some castes which are socially and educationally backwards but not coming under SC or ST. Such classes are described as other Backward classes. This list of OBCs will be changing from time to time. Some castes may be getting removed and some may be getting added.
Thuluva Vellalar is included in both the BC category and OBC category as per the information available.

OBC and BC indicate to same underprivileged people for which Govt provides reservations. Central Govt publishes a list in this regard where state wise mentioning of categories entitled as OBC are given in details. One can see that at the Govt site https://pib.gov.in/newsite/PrintRelease.aspx?relid=124804
BC category is already worked out by the various states and reservations to that extent would be available to them. The OBC list added by centre is over and above the BC list prepared by the states. In official working generally both the categories are mentioned as BC only for sake of convenience and avoid confusion.
As per the list in the Govt site http://www.bcmbcmw.tn.gov.in/bclist.htm, Thulluva Vellalar falls in BC category.

OBC is the abbreviation of other backward class while BC stands for Backward class. Both are almost same. Both belong to underprivileged society. Both include all which are economically and socially backwards. BC category contains communities that are classified as economically and educationally backward by state Govt. Whereas, OBC category contains communities that are classified as economically and educationally backward by central Govt. Of India. OBC gets more benefit than BC in terms of education and position.

Thuluva Vellalar is included in both categories as per the information.