Difference

Theethou, and thine (or thy) are Early Modern English second person singular pronouns. Thou is the subject form (nominative), thee is the object form, and thy/thine is the possessive form.

Before they all merged into the catch-all form you, English second person pronouns distinguished between nominative and objective, as well as between singular and plural (or formal):

thou - singular informal, subject (Thou art here. = You are here.)
thee - singular informal, object (He gave it to thee.)
ye - plural or formal, subject
you - plural or formal, object

Familiar, Offensive (don't thee thou me, thee thou thissen)

From: https://english.stackexchange.com/a/118058/146585
‘Thou’ is historically perceived in Yorkshire (England) as being disrespectful, or over-familiar in a formal context, e.g. if used to address a teacher, or upon greeting a stranger… However, ‘thee’ is perceived to be more respectful, as with the French usage of the words ‘vous’ and ‘tu’, of which ‘tu’ is regarded as offensive if used inappropriately (another conversation altogether). Barnsley folk are especially well know for having the bad habit of using ‘thou’, including one instance I’ve heard of with a French teacher, who mistakenly believed it to be endearing, and quickly chastised her pupils once she was put in the picture.

A classic Yorkshire phrase, often attributed to Ossett:

_Don't thee thou me, thee thou thissen, and 'ow tha likes thee thouing._ (Don't you thou me, you thou yourself, and see how you like it!)