I think najaB has covered the issues here. The procedure at trial is to determine whether the accused is Guilty or Not Guilty without any consideration of the possible penalty which might follow from of a finding of Guilt, and to do so only on the basis of the Evidence presented and on the authorities presented in the form of statute, common law and relevant prior judgements. That is the 'judgement', determined on the facts and the law.
Only then, and only if the finding was one of 'Guilt', will the Court move on to the question of 'sentencing', which includes fines, terms of imprisonment, and other possible orders. There are published guidelines for the 'sentences' that follow certain offences and which take account of factors in mitigation, and so it becomes possible to claim that a Court had made an error in determining the 'sentence' in any particular case. In such cases, the sentence can be Appealled (and do so without re-trying the facts of the accusation).
The Prosecution will also claim their costs after a conviction, and it is for the Court to decide whether or not to pass that full amount onto the loosing party. That decision too can be Appealled, without a re-trial of the facts.
[This is just a brief summary of the distinction and is not exhaustive].
Yes, it's not uncommon for an accused person to Appeal against 'sentence' and then on failing, walk away with an even higher fine or term of custody.
Once the argument that a Judge or Magistrate had erred in determining a penalty is won, the Appeal Judge will then look at the sentence afresh - and will impose an alternative sentence which may be higher or lower than the original sentence.
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