Subman, Welcome to the hobby. Back in the 60's and 70's there was a company called 'Thomson Center'. Not certain they are still around today but the one I had was a rather plain rifle of above standard quality. The rifle in the first photo marked 'Warranted' looks similar in style to the 'Thompson Center' product, however, it has been altered with the carving and brass work. The alteration was common as shooters wanted to dandy up there guns. That is not a negative in your case as my comment only refers the habit of alteration. My gun was flint and shot very well. Basically, it was all I could afford at the time.
'Warranted': This is not a maker nor the gunsmith or the company who made your gun. It is simply a statement indicating the lock left the factory in working order. The stamp was common along with the lock makers name in the 18th and 19th centuries, ie: Bishop Warranted. Bishop being the lock maker and in most cases not the gunsmith who built the gun. Early lock making was a 'cottage industry' in England and several other European countries. English locks from the 18th and 19th centuries were distinctively different in appearance than German or American hand made locks. A whole lot to learn regarding early lock making but it doesn't apply here as your gun is modern made.
If you are anywhere near being new to 'Black Powder' shooting I suggest you take both guns to a competent local gunsmith and seek advice as to their working condition. Best to be safe rather than sorry. HIB