That bit about higher pay and no benefits sounds a bit concerning. You need to find out if you are an employee of the company you work at, or a freelance supplier. You could be freelance at the company you work at, and employed by an umbrella company.
If it's all new, you can sort everything easily. If it goes on over time, problems can develop.
Again, talk to your boss, and an accountant if needed, or of course somebody else here who can offer advice. Everything Mr or Mrs Seahorse said is correct.