Online: An online system is usually a web or cloud orientated portal so you will definitely need an internet connection. The end user then inputs their receipts and invoices manually.
The software will link to your business bank account and most packages offer real time updates of your finances 24/7 and an app for phone or tablet. Many online packages will offer a free trial initially but expect to then pay a monthly subscription dependent on what features you require. Look for benefits such as ease of use and customer support such as phone and email and allow yourself time for learning the software and to plan time aside for admin in your work schedule. You will still have to submit your monthly financial statement for your accountant. Although the software can give you a snapshot of your accounts the down side is that you still have offline paperwork to do as well.
Offline: An offline system usually involves a lot more admin and paperwork compared to an online system, it can exist either as a spreadsheet whereby you input all the data yourself (note you will still need a computer or tablet to do this) or as a bookkeeping service with which you submit all invoices and receipts to your accountant each month. Some accountants will offer bookkeeping as well but expect to pay for that service. The disadvantage of offline compared to online is that you cannot see your accounts in real time and will not know how much you are allowed to spend and how much to save ie: tax