Latner and your accounting system (Xero, MYOB or Sage Intacct) each build the invoice PDF from their own template. Latner doesn't send its invoice PDF across - only the invoice data syncs: the customer, invoice number, reference, dates or payment terms, line descriptions, quantities, amounts, account codes and tax codes. Your accounting system then lays that data out with its own invoice template, so the logo, layout and wording around the figures will differ from Latner's PDF, and anything Latner's template prints that isn't part of the synced data won't appear on the accounting system's version.
Latner's layout comes from its PDF templates, under Security › Settings › PDF Templates. For the standard templates you can change the PDF Logo Image, Primary PDF Theme Color and PDF Header Content there. If you use a custom invoice template, contact Latner support to change its layout. Changing the invoice template in Xero or MYOB doesn't change Latner's PDF, and changing Latner's PDF templates doesn't change theirs.
The customer, lines and amounts on both come from the same Latner invoice. If the amounts themselves don't match, that's a sync issue rather than a template difference - check the Integration Syncs tab on the invoice and re-sync it.