您可以使用on_message_delete和on_message_edit，就像您正在使用的一样，然后您应该将函数指定为message而不是ctx。
消息删除示例：

@client.event
async def on_message_delete(message):
    embed=discord.Embed(title="{} deleted a message".format(message.member.name), 
    description="", color="Blue")
    embed.add_field(name= message.content ,value="This is the message that he has 
    deleted", 
    inline=True)
    channel=client.get_channel(channel_id)
await channel.send(embed=embed)

消息编辑示例：

@client.event
async def on_message_edit(message_before, message_after):
    embed=discord.Embed(title="{} edited a 
    message".format(message_before.member.name), 
    description="", color="Blue")
    embed.add_field(name= message_before.content ,value="This is the message before 
    any edit", 
    inline=True)
    embed.add_field(name= message_after.content ,value="This is the message after the 
    edit", 
    inline=True)
    channel=client.get_channel(channel_id)
await channel.send(embed=embed)

上面显示的方式将不会工作的时候，使这篇文章。这就是为什么我已经编辑它，使它会。
行：

embed=discord.Embed(title="{} edited a 
    message".format(message_before.member.name), 
    description="", color="Blue")

因为message没有member属性，所以它不起作用。它也不起作用，因为你不能将颜色设置为Blue或没有整数转换的字符串。最好的方法是定义一个十六进制，像这样输入color=0xFF0000，这样它就变成了红色。
整行字都变了：

embed = discord.Embed(title="{} deleted a message".format(message.author.name),
                      description="", color=0xFF0000)

以下是经过编辑后可以正常工作的两个完整命令。

@client.event
async def on_message_delete(message):
    embed = discord.Embed(title="{} deleted a message".format(message.author.name),
                          description="", color=0xFF0000)
    embed.add_field(name=message.content, value="This is the message that he has deleted",
                    inline=True)
    channel = client.get_channel(channelid)
    await channel.send(channel, embed=embed)

@client.event
async def on_message_edit(message_before, message_after):
    embed = discord.Embed(title="{} edited a message".format(message_before.author.name),
                          description="", color=0xFF0000)
    embed.add_field(name=message_before.content, value="This is the message before any edit",
                    inline=True)
    embed.add_field(name=message_after.content, value="This is the message after the edit",
                    inline=True)
    channel = client.get_channel(channelid)
    await channel.send(channel, embed=embed)

我会在你的代码顶部定义你想使用的通道，就像这样。

logging_channel = channelID
# then at your two commands do this:
global logging_channel